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This paper presents the multiplicity of neutral and charged hadrons produced in 90 GeV$/c$ proton-carbon interactions from a dataset taken by the NA61/SHINE experiment in 2017. Particle identification via dE/dx was performed for the charged hadrons $\pi^\pm$, $K^\pm$, and $p / \bar{p}$; the neutral hadrons $K^0_S$, $\Lambda$, and $\bar{\Lambda}$ were identified via an invariant mass analysis of their decays to charged hadrons. Double-differential multiplicity results as a function of laboratory momentum and polar angle are presented for each particle species; these results provide vital constraints on the predicted neutrino beam flux for current and future long-baseline neutrino oscillation experiments.

The Betti tables of a multigraded module encode the grades at which there is an algebraic change in the module. Multigraded modules show up in many areas of pure and applied mathematics, and in particular in topological data analysis, where they are known as persistence modules, and where their Betti tables describe the places at which the homology of filtered simplicial complexes change. Although Betti tables of singly and bigraded modules are already being used in applications of topological data analysis, their computation in the bigraded case (which relies on an algorithm that is cubic in the size of the filtered simplicial complex) is a bottleneck when working with large datasets. We show that, in the special case of $0$-dimensional homology (which is relevant for clustering and graph classification) the Betti tables of a bigraded module can be computed in log-linear time. We also consider the problem of computing minimal presentations, and show that a minimal presentation of $0$-dimensional persistent homology can be computed in quadratic time, regardless of the grading poset., Comment: 19 pages, 1 figure

Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. Even though it is known that the barcode for a zigzag filtration with $m$ insertions and deletions can be computed in $O(m^\omega)$ time, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $O(m^3)$ time, which can be improved to $O(m^\omega)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^2n)$ time algorithm for this problem, where $n\leq m$ is the size of the largest complex in the filtration.

We generalize the recently discovered planar decomposition (Kauffman bracket) for the HOMFLY polynomials of bipartite knot/link diagrams to (anti)symmetrically colored HOMFLY polynomials. Cabling destroys planarity, but it is restored after projection to (anti)symmetric representations. This allows to go beyond arborescent calculus, which so far produced the majority of results for colored polynomials. Technicalities include combinations of projectors, and these can be handled rigorously, without any guess-work -- what can be also useful for other considerations, where reliable quantization was so far unavailable. We explicitly provide simple examples of calculation of the HOMFLY polynomials in symmetric representations with the use of our planar technique. These examples reveal what we call the bipartite evolution and the bipartite decomposition of squares of $\mathcal{R}$-matrices eigenvalues in the antiparallel channel., Comment: 26 pages

Keyphrase selection is a challenging task in natural language processing that has a wide range of applications. Adapting existing supervised and unsupervised solutions for the Russian language faces several limitations due to the rich morphology of Russian and the limited number of training datasets available. Recent studies conducted on English texts show that large language models (LLMs) successfully address the task of generating keyphrases. LLMs allow achieving impressive results without task-specific fine-tuning, using text prompts instead. In this work, we access the performance of prompt-based methods for generating keyphrases for Russian scientific abstracts. First, we compare the performance of zero-shot and few-shot prompt-based methods, fine-tuned models, and unsupervised methods. Then we assess strategies for selecting keyphrase examples in a few-shot setting. We present the outcomes of human evaluation of the generated keyphrases and analyze the strengths and weaknesses of the models through expert assessment. Our results suggest that prompt-based methods can outperform common baselines even using simple text prompts., Comment: The 12th International Conference on Analysis of Images, Social Networks and Texts (AIST'2024)

Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to compute in parallel because it relies on global connectivity of the data. We propose a new algorithm to compute persistent cohomology in the distributed setting. It combines domain and range partitioning. The former is used to reduce and sparsify the coboundary matrix locally. After this initial local reduction, we redistribute the matrix across processors for the global reduction. We experimentally compare our cohomology algorithm with DIPHA, the only publicly available code for distributed computation of persistent (co)homology; our algorithm demonstrates a significant improvement in strong scaling., Comment: 11 pages, 16 figures

Generative Flow Networks (GFlowNets) are a family of generative models that learn to sample objects with probabilities proportional to a given reward function. The key concept behind GFlowNets is the use of two stochastic policies: a forward policy, which incrementally constructs compositional objects, and a backward policy, which sequentially deconstructs them. Recent results show a close relationship between GFlowNet training and entropy-regularized reinforcement learning (RL) problems with a particular reward design. However, this connection applies only in the setting of a fixed backward policy, which might be a significant limitation. As a remedy to this problem, we introduce a simple backward policy optimization algorithm that involves direct maximization of the value function in an entropy-regularized Markov Decision Process (MDP) over intermediate rewards. We provide an extensive experimental evaluation of the proposed approach across various benchmarks in combination with both RL and GFlowNet algorithms and demonstrate its faster convergence and mode discovery in complex environments.

We prove that normalized colored Alexander polynomial (the $A \rightarrow 1$ limit of colored HOMFLY-PT polynomial) evaluated for one-hook (L-shape) representation R possesses scaling property: it is equal to the fundamental Alexander polynomial with the substitution $q \rightarrow q^{|R|}$. The proof is simple and direct use of Reshetikhin-Turaev formalism to get all required R-matrices., Comment: 20 pages

This article extends the study of dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only two are irreducible: the linearized rotation number at the fixed point and a nonlinear parameter representing the ratio of terms in the biquadratic invariant. Through a detailed analysis, we classify regimes of stable motion, provide exact solutions to the mapping equations, and derive a canonical set of action-angle variables, offering analytical expressions for the rotation number and nonlinear tune shift. We further establish connections between general standard-form mappings and the symmetric McMillan map, using the area-preserving H\'eon map and accelerator lattices with thin sextupole magnet as representative case studies. Our results show that, despite being a second-order approximation, the symmetric McMillan map provides a highly accurate depiction of dynamics across a wide range of system parameters, demonstrating its practical relevance in both theoretical and applied contexts.

Quite some years ago, Oleg Chalykh has built a nice theory from the observation that the Macdonald polynomial reduces at $t=q^{-m}$ to a sum over permutations of simpler polynomials called Baker-Akhiezer functions, which can be unambiguously constructed from a system of linear difference equations. Moreover, he also proposed a generalization of these polynomials to the twisted Baker-Akhiezer functions. Recently, in a private communication Oleg suggested that these twisted Baker-Akhiezer functions could provide eigenfunctions of the commuting Hamiltonians associated with the $(-1,a)$ rays of the Ding-Iohara-Miki algebra. In the paper, we discuss this suggestion and some evidence in its support., Comment: 14 pages, LaTeX

Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise approximations have also received significant attention in the literature. In this paper, we propose an accelerated alternating minimization algorithm for solving the problem of low-rank approximation of matrices in the Chebyshev norm. Through the numerical evaluation we demonstrate the effectiveness of the proposed procedure for large-scale problems. We also theoretically investigate the alternating minimization method and introduce the notion of a $2$-way alternance of rank $r$. We show that the presence of a $2$-way alternance of rank $r$ is the necessary condition of the optimal low-rank approximation in the Chebyshev norm and that all limit points of the alternating minimization method satisfy this condition.

A typical example of superintegrability is provided by expression of the Hopf link hyperpolynomial in an arbitrary representation through a pair of the Macdonald polynomials at special points. In the simpler case of the Hopf link HOMFLY-PT polynomial and a pair of the Schur functions, it is a relation in the unitary matrix model. We explain that the Cherednik-Mehta-Macdonald (CMM) identity for bilinear Macdonald residues with an elliptic weight function is nothing but a reformulation of these same formulas. Their lifting to arbitrary knots and links, even torus ones remains obscure., Comment: 12 pages

Novel CaV1-xWxO3 (0.1 <= x <= 0.33) oxides with an orthorhombically distorted perovskite structure of GdFeO3 type have been synthesized. These compounds contain in B-position W6+ and V cations in an oxidation state between 4+ (CaVO3) and 3+ (x=0.33). CaV0.9W0.1O3 compound possesses metallic type of conductivity and Pauli paramagnetism. The intermediate compositions are between bad metal and semiconducting type of behavior with paramagnetic response. CaV0.67W0.33O3 is a Mott insulator with localized V3+ moments coupled by strong antiferromagnetic interactions. It demonstrates the reduction of effective magnetic moment at high temperatures and canonical spin glass state formation with the freezing temperature Tg = 27.5 K seen in dc - and ac - magnetic susceptibility. Disorder in the magnetic subsystem induces a broad Schottky type anomaly in magnetic contribution of the heat capacity at Tmax = 34 K., Comment: 12 pages, 6 figures

The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning, can be cast and solved as an SPP in GCS, yielding lower-cost solutions and faster runtimes than state-of-the-art algorithms. In this paper, we are motivated by motion planning of robot arms that must operate swiftly in static environments. We consider a multi-query extension of the SPP in GCS, where the goal is to efficiently precompute optimal paths between given sets of initial and target conditions. Our solution consists of two stages. Offline, we use semidefinite programming to compute a coarse lower bound on the problem's cost-to-go function. Then, online, this lower bound is used to incrementally generate feasible paths by solving short-horizon convex programs. For a robot arm with seven joints, our method designs higher quality trajectories up to two orders of magnitude faster than existing motion planners., Comment: To appear in: The International Workshop on the Algorithmic Foundations of Robotics, WAFR 2024

Keyphrase selection plays a pivotal role within the domain of scholarly texts, facilitating efficient information retrieval, summarization, and indexing. In this work, we explored how to apply fine-tuned generative transformer-based models to the specific task of keyphrase selection within Russian scientific texts. We experimented with four distinct generative models, such as ruT5, ruGPT, mT5, and mBART, and evaluated their performance in both in-domain and cross-domain settings. The experiments were conducted on the texts of Russian scientific abstracts from four domains: mathematics & computer science, history, medicine, and linguistics. The use of generative models, namely mBART, led to gains in in-domain performance (up to 4.9% in BERTScore, 9.0% in ROUGE-1, and 12.2% in F1-score) over three keyphrase extraction baselines for the Russian language. Although the results for cross-domain usage were significantly lower, they still demonstrated the capability to surpass baseline performances in several cases, underscoring the promising potential for further exploration and refinement in this research field., Comment: DAMDID-2024

The paper is concerned with Lax representations for the three-dimensional Euler--Helmholtz equation. We show that the parameter in the Lax representation from Theorem 3 in [15] is non-removable. Then we present two new Lax representations with non-removable parameters.

Robustness is critical for machine learning (ML) classifiers to ensure consistent performance in real-world applications where models may encounter corrupted or adversarial inputs. In particular, assessing the robustness of classifiers to adversarial inputs is essential to protect systems from vulnerabilities and thus ensure safety in use. However, methods to accurately compute adversarial robustness have been challenging for complex ML models and high-dimensional data. Furthermore, evaluations typically measure adversarial accuracy on specific attack budgets, limiting the informative value of the resulting metrics. This paper investigates the estimation of the more informative adversarial distance using iterative adversarial attacks and a certification approach. Combined, the methods provide a comprehensive evaluation of adversarial robustness by computing estimates for the upper and lower bounds of the adversarial distance. We present visualisations and ablation studies that provide insights into how this evaluation method should be applied and parameterised. We find that our adversarial attack approach is effective compared to related implementations, while the certification method falls short of expectations. The approach in this paper should encourage a more informative way of evaluating the adversarial robustness of ML classifiers., Comment: Accepted manuscript at International Mechanical Engineering Congress and Exposition IMECE2024

This review paper describes the energy-upgraded CEBAF accelerator. This superconducting linac has achieved 12 GeV beam energy by adding 11 new high-performance cryomodules containing eighty-eight superconducting cavities that have operated CW at an average accelerating gradient of 20 MV/m. After reviewing the attributes and performance of the previous 6 GeV CEBAF accelerator, we discuss the upgraded CEBAF accelerator system in detail with particular attention paid to the new beam acceleration systems. In addition to doubling the acceleration in each linac, the upgrade included improving the beam recirculation magnets, adding more helium cooling capacity to allow the newly installed modules to run cold, adding a new experimental hall, and improving numerous other accelerator components. We review several of the techniques deployed to operate and analyze the accelerator performance, and document system operating experience and performance. In the final portion of the document, we present much of the current planning regarding projects to improve accelerator performance and enhance operating margins, and our plans for ensuring CEBAF operates reliably into the future. For the benefit of potential users of CEBAF, the performance and quality measures for beam delivered to each of the experimental halls is summarized in the appendix., Comment: 66 pages, 73 figures, 21 tables

Superconducting nanowire single-photon detectors are widely used for detecting individual photons across various wavelengths from ultraviolet to near-infrared range. Recently, there has been increasing interest in enhancing their sensitivity to single photons in the mid-infrared spectrum, driven by applications in quantum communication, spectroscopy and astrophysics. Here, we present our efforts to expand the spectral detection capabilities of U-shaped NbTiN-based superconducting nanowire single-photon detectors, fabricated in a 2-wire configuration on a silicon-on-insulator substrate, into the mid-infrared range. We demonstrate saturated internal detection efficiency extending up to a wavelength of 3.5 {\mu}m for a 5 nm thick and 50 nm wide NbTiN nanowire with a dark count rate less than 10 counts per second at 0.9 K and a rapid recovery time of 4.3 ns. The detectors are engineered for integration on waveguides in a silicon-on-insulator platform for compact, multi-channel device applications., Comment: 5 figures, 7 pages

We extend the study of banana diagrams in coordinate representation to the case of curved space-times. If the space is harmonic, the Green functions continue to depend on a single variable -- the geodesic distance. But now this dependence can be somewhat non-trivial. We demonstrate that, like in the flat case, the coordinate differential equations for powers of Green functions can still be expressed as determinants of certain operators. Therefore, not-surprisingly, the coordinate equations remain straightforward -- while their reformulation in terms of momentum integrals and Picard-Fuchs equations can seem problematic. However we show that the Feynman parameter representation can also be generalized, at least for banana diagrams in simple harmonic spaces, so that the Picard-Fuchs equations retain their Euclidean form with just a minor modification. A separate story is the transfer to the case when the Green function essentially depends on several rather than a single argument. In this case, we provide just one example, that the equations are still there, but conceptual issues in the more general case will be discussed elsewhere.

Chern-Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms. In this paper we discuss opposite problem of finding Chern-Simons level $k$ in the unknown material. For this purpose, we use the previously derived braiding rules for Chern-Simons $SU(2)_k$ anyons. Using certain operations (turnarounds) on three anyons, one can measure probabilities of annihilation of pairs of anyons, which depend on the parameter of the theory. Therefore, Chern-Simons level $k$ can be found from such an experiment. It is implied that anyons additionally possess certain properties which are required for topological quantum computations., Comment: 12 pages, 13 figures

A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum $A$- and $C$-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in much simpler terms, what could make these techniques available to a broader audience. To avoid overloading of the presentation, only the case of the colored Jones polynomial for the trefoil knot is considered, though various generalizations are straightforward. Restriction to solely Jones polynomials (rather than full HOMFLY-PT) is related to a serious simplification, provided by the use of Kauffman calculus. Going beyond looks realistic, however it remains a problem, both challenging and promising., Comment: 16 pages

We propose the extension of the position space approach to Feynman integrals from the banana family to generic Feynman diagrams. Our approach is based on getting rid of integration in position space and then writing differential equations for the products of propagators defined for any graph. We employ the so-called ''bananization'' to start with simple Feynman graphs and further substituting each edge with a multiple one. We explain how the previously developed theory of banana diagrams can be used to describe what happens to the differential equations (Ward identities) on Feynman diagrams after this transformation. Our approach works for generic enough (large enough) dimension and masses. We expect that after Fourier transform our equations should be related to the Picard-Fuchs equations. Therefore, we describe the challenges of Fourier transform that arise in our approach.

Traps and structural defects at the hole and electron transport interfaces of the microcrystalline absorber limits the efficiency and long-term stability of perovskite solar cells (PSCs) due to accumulation of the ionic clusters, non-radiative recombination and electrochemical corrosion. Surface engineering using self-assembled monolayers (SAM) was considered as an effective strategy for modification of charge-collection junctions. In this work, we demonstrate the first report about complex integration of a SAM for double-side passivation in p-i-n PSCs. Integrating the novel 5-(4-[bis(4-fluorophenyl)amino]phenyl)thiophene-2-carboxylic acid (FTPATC) as a fluorinated SAM at the hole-transport interface reduced potential barriers and lattice stresses in the absorber. At the electron-transport side, FTPATC interacted with the A-site cations of the perovskite molecule (Cs, formamidinium), inducing a dipole for defect compensation. Using the passivation approach with fluorinated SAM demonstrated benefits in the gain of the output performance up to 22.2%. The key-advantage of double-side passivation was confirmed by the enhanced stability under continuous light-soaking (1-sun equivalent, 65 C, ISOS-L-2), maintaining 88% of the initial performance over 1680 hours and thermal stabilization under harsh heating at 90 C.

Predicting high-fidelity ground motions for future earthquakes is crucial for seismic hazard assessment and infrastructure resilience. Conventional empirical simulations suffer from sparse sensor distribution and geographically localized earthquake locations, while physics-based methods are computationally intensive and require accurate representations of Earth structures and earthquake sources. We propose a novel artificial intelligence (AI) simulator, Conditional Generative Modeling for Ground Motion (CGM-GM), to synthesize high-frequency and spatially continuous earthquake ground motion waveforms. CGM-GM leverages earthquake magnitudes and geographic coordinates of earthquakes and sensors as inputs, learning complex wave physics and Earth heterogeneities, without explicit physics constraints. This is achieved through a probabilistic autoencoder that captures latent distributions in the time-frequency domain and variational sequential models for prior and posterior distributions. We evaluate the performance of CGM-GM using small-magnitude earthquake records from the San Francisco Bay Area, a region with high seismic risks. CGM-GM demonstrates a strong potential for outperforming a state-of-the-art non-ergodic empirical ground motion model and shows great promise in seismology and beyond.

The theory of the Kauffman bracket, which describes the Jones polynomial as a sum over closed circles formed by the planar resolution of vertices in a knot diagram, can be straightforwardly lifted from sl(2) to sl(N) at arbitrary N -- but for a special class of bipartite diagrams made entirely from the anitparallel lock tangle. Many amusing and important knots and links can be described in this way, from twist and double braid knots to the celebrated Kanenobu knots for even parameters -- and for all of them the entire HOMFLY polynomials possess planar decomposition. This provides an approach to evaluation of HOMFLY polynomials, which is complementary to the arborescent calculus, and this opens a new direction to homological techniques, parallel to Khovanov-Rozansky generalisations of the Kauffman calculus. Moreover, this planar calculus is also applicable to other symmetric representations beyond the fundamental one, and to links which are not fully bipartite what is illustrated by examples of Kanenobu-like links., Comment: 33 pages, published version

We consider a statistical mechanical model of a generic flexible polyelectrolyte, comprised of identically charged monomers with long range electrostatic interactions, and short-range interactions quantified by a disorder field along the polymer contour sequence, which is randomly quenched. The free energy and the monomer density profile of the system for no electrolyte screening are calculated in the case of a system composed of two infinite planar bounding surfaces with an intervening oppositely charged polyelectrolyte chain. We show that the effect of the contour sequence disorder, mediated by short-range interactions, leads to an enhanced localization of the polyelectrolyte chain and a first order phase transition at a critical value of the inter-surface spacing. This phase transition results in an abrupt change of the pressure from negative to positive values, effectively eliminating polyelectrolyte mediated bridging attraction.

In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack and Macdonald families so that the new polynomials depend on odd Grassmann variables as well. Members of these families are labeled by respective modifications of Young diagrams. We show that the super-Macdonald polynomials form a representation of a super-algebra analog $\mathsf{T}(\widehat{\mathfrak{gl}}_{1|1})$ of Ding-Ioahara-Miki (quantum toroidal) algebra, emerging as a BPS algebra of D-branes on a conifold. A supersymmetric modification for Young tableaux and Kostka numbers are also discussed., Comment: 26 pages, 2 figures, v2: typos corrected, references added

We introduce generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables: usual $p_k$ variables are accompanied by anti-commuting Grassmann variables $\theta_k$. Starting from recently defined super-Schur polynomials and exploiting orthogonality relations with triangular decompositions we are able to fully determine super-Macdonald polynomials. These new polynomials have similar properties to canonical Macdonald polynomials -- they respect two different orderings in the set of (super)-Young diagrams simultaneously.

Halide perovskite-based photodiodes are promising for efficient detection across a broad spectral range. Perovskite absorber thin-films have a microcrystalline morphology, characterized by a high density of surface states and defects at inter-grain interfaces. In this work, we used dielectric-ferroelectric poly(vinylidene-fluoride-trifluoroethylene-P(VDF-TrFE) to modify the bulk interfaces and electron transport junction in p-i-n perovskite photodiodes. Our complex work demonstrates that interface engineering with P(VDF-TrFE) induces significant Fermi level pinning, reducing from 4.85 eV for intrinsic perovskite to 4.28 eV for the configuration with dielectric interlayers. The integration of P(VDF-TrFE) into the perovskite film did not affect the morphology and crystal structure, but significantly changed the charge transport and device performance. IV curve analysis and 2-diode model calculations showed enhanced shunt properties, a decreased non-ideality factor, and reduced saturation dark current. We have shown that the complex introduction of P(VDF-TrFE) into the absorbers bulk and on its surface is essential to reduce the impact of the trapping processes. For P(VDF-TrFE) containing devices, we increased the specific detectivity from 10^11 to 10^12 Jones, expanded the linear dynamic range up to 100 dB, and reduced the equivalent noise power to 10^-13 W*Hz^-0.5. Reducing non-radiative recombination contributions significantly enhanced device performance, improving rise/fall times from 6.3/10.9 us to 4.6/6.5 us. The cut-off frequency (3dB) increased from 64.8 kHz to 74.8 kHz following the introduction of the dielectric. These results provide new insights into the use of organic dielectrics and an improved understanding of trap-states and ion defect compensation for detectors based on perovskite heterostructures.

In this note, we aim to review algorithms for constructing crystal representations of quiver Yangians in detail. Quiver Yangians are believed to describe an action of the BPS algebra on BPS states in systems of D-branes wrapping toric Calabi-Yau three-folds. Crystal modules of these algebras originate from molten crystal models for Donaldson-Thomas invariants of respective three-folds. Despite the fact that this subject was originally at the crossroads of algebraic geometry with effective supersymmetric field theories, equivariant toric action simplifies applied calculations drastically. So the sole pre-requisite for this algorithm's implementation is linear algebra. It can be easily taught to a machine with the help of any symbolic calculation system. Moreover, these algorithms may be generalized to toroidal and elliptic algebras and exploited in various numerical experiments with those algebras. We illustrate the work of the algorithms in applications to simple cases of $\mathsf{Y}(\mathfrak{sl}_2)$, $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1})$ and $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1|1})$., Comment: 41 pages, 9 figures

We extend our consideration of commutative subalgebras (rays) in different representations of the $W_{1+\infty}$ algebra to the elliptic Hall algebra (or, equivalently, to the Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$). Its advantage is that it possesses the Miki automorphism, which makes all commutative rays equivalent. Integrable systems associated with these rays become finite-difference and, apart from the trigonometric Ruijsenaars system not too much familiar. We concentrate on the simplest many-body and Fock representations, and derive explicit formulas for all generators of the elliptic Hall algebra $e_{n,m}$. In the one-body representation, they differ just by normalization from $z^nq^{m\hat D}$ of the $W_{1+\infty}$ Lie algebra, and, in the $N$-body case, they are non-trivially generalized to monomials of the Cherednik operators with action restricted to symmetric polynomials. In the Fock representation, the resulting operators are expressed through auxiliary polynomials of $n$ variables, which define weights in the residues formulas. We also discuss $q,t$-deformation of matrix models associated with constructed commutative subalgebras., Comment: 51 pages, LaTeX

Generative Flow Networks (GFlowNets) treat sampling from distributions over compositional discrete spaces as a sequential decision-making problem, training a stochastic policy to construct objects step by step. Recent studies have revealed strong connections between GFlowNets and entropy-regularized reinforcement learning. Building on these insights, we propose to enhance planning capabilities of GFlowNets by applying Monte Carlo Tree Search (MCTS). Specifically, we show how the MENTS algorithm (Xiao et al., 2019) can be adapted for GFlowNets and used during both training and inference. Our experiments demonstrate that this approach improves the sample efficiency of GFlowNet training and the generation fidelity of pre-trained GFlowNet models., Comment: ICML 2024 SPIGM Workshop

Character expansions are among the most important approaches to modern quantum field theory, which substitute integrals by combinations of peculiar special functions from the Schur-Macdonald family. These formulas allow various deformations, which are not transparent in integral formulation. We analyze from this point of view the Itzykson-Zuber integral over unitary matrices which is exactly solvable, but difficult to deform in $\beta$ and $(q,t)$ directions. Character expansion straightforwardly resolves this problem. However, taking averages with the so defined measure can look problematic, because integrals of individual expansion terms often diverge and well defined is only the sum of them. We explain a way to overcome this problem by Gaussian regularization, which can have a broad range of further applications., Comment: 13 pages

In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symmetric McMillan maps, characterized by a single intrinsic parameter. While these systems find numerous applications across various domains of mathematics and physics, some of their dynamical properties remain unexplored. We aim to bridge this gap by providing a comprehensive description of all stable trajectories, including the parametrization of invariant curves, Poincar\'e rotation numbers, and canonical action-angle variables. In the second part, we establish connections between these maps and general chaotic maps in standard form. Our investigation reveals that the McMillan sextupole and octupole serve as first-order approximations of the dynamics around the fixed point, akin to the linear map and quadratic invariant (known as the Courant-Snyder invariant in accelerator physics), which represents zeroth-order approximations (referred to as linearization). Furthermore, we propose a novel formalism for nonlinear Twiss parameters, which accounts for the dependence of rotation number on amplitude. This stands in contrast to conventional betatron phase advance used in accelerator physics, which remains independent of amplitude. Notably, in the context of accelerator physics, this new formalism demonstrates its capability in predicting dynamical aperture around low-order resonances for flat beams, a critical aspect in beam injection/extraction scenarios.

In this paper we discuss an approach to calculate knot polynomials on a photonic processor. Calculations of knot polynomials is a computationally difficult problem and therefore it is interesting to use new advanced calculation methods to find them. Here we present a proof of concept by calculating the simplest knot polynomial of the trefoil knot in fundamental representation. This approach, however, can easily be generalized to more complex knots and representations. Same operators can also be realized on a quantum computer with the same effect., Comment: 5 pages, 2 figures

In this paper we discuss how to use arborescent knots to construct entangled multi-qubit states. We show that Bell-states, GHZ-states and cluster states can be constructed from such knots. The latter are particularly interesting since they form a base for the measurement-based quantum computers., Comment: 8 pages, 7 figures

In situ approaches can accelerate the pace of scientific discoveries by allowing scientists to perform data analysis at simulation time. Current in situ workflow systems, however, face challenges in handling the growing complexity and diverse computational requirements of scientific tasks. In this work, we present Wilkins, an in situ workflow system that is designed for ease-of-use while providing scalable and efficient execution of workflow tasks. Wilkins provides a flexible workflow description interface, employs a high-performance data transport layer based on HDF5, and supports tasks with disparate data rates by providing a flow control mechanism. Wilkins seamlessly couples scientific tasks that already use HDF5, without requiring task code modifications. We demonstrate the above features using both synthetic benchmarks and two science use cases in materials science and cosmology.

We continue the development of a position space approach to equations for Feynman multi-loop integrals. The key idea of the approach is that unintegrated products of Greens functions in position space are still loop integral in momentum space. The natural place to start are the famous banana diagrams, which we explore in this paper. In position space, these are just products of $n$ propagators. Firstly, we explain that these functions satisfy an equation of order $2^n$. These should be compared with Picard-Fuchs equations derived for the momentum space integral. We find that the Fourier transform of the position space operator contains the Picard-Fuchs one as a rightmost factor. The order of these operators is a special issue, especially since the order in momentum space is governed by degree in $x$ in position space. For the generic mass case this factorization pattern is complicated and it seems like the order of the Fourier transformed position space operators is much bigger than that of the Picard-Fuchs. Furthermore, one may ask what happens if after factorization we take the Picard-Fuchs operators back into position space. We discover that the result is again factorized, with the rightmost factor being the original position space equation. We demonstrate how this works in examples and discuss implications for more sophisticated Feynman integrals.

BPS states in supersymmetric theories can admit additional algebro-geometric structures in their spectra, described as quiver Yangian algebras. Equivariant fixed points on the quiver variety are interpreted as vectors populating a representation module, and matrix elements for the generators are then defined as Duistermaat-Heckman integrals in the vicinity of these points. The well-known wall-crossing phenomena are that the fixed point spectrum establishes a dependence on the stability (Fayet-Illiopolous) parameters $\zeta$, jumping abruptly across the walls of marginal stability, which divide the $\zeta$-space into a collection of stability chambers -- ``phases'' of the theory. The standard construction of the quiver Yangian algebra relies heavily on the molten crystal model, valid in a sole cyclic chamber where all the $\zeta$-parameters have the same sign. We propose to lift this restriction and investigate the effects of the wall-crossing phenomena on the quiver Yangian algebra and its representations -- starting with the example of affine super-Yangian $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1|1})$. In addition to the molten crystal construction more general atomic structures appear, in other non-cyclic phases (chambers of the $\zeta$-space). We call them glasses and also divide in a few different classes. For some of the new phases we manage to associate an algebraic structure again as a representation of the same affine Yangian $\mathsf{Y}(\widehat{\mathfrak{gl}}_{1|1})$. This observation supports an earlier conjecture that the BPS algebraic structures can be considered as new wall-crossing invariants., Comment: 36 pages, 7 figures, minor corrections, references added

High-intensity lasers require suppression of prepulses and other non-ideal temporal structure to avoid target disruption before the arrival of the main pulse. To address this, we demonstrate that ionization gratings act as a controllable optical switch for high-power light with a temporal contrast improvement of at least $3\times10^5$ and a switching time less than 500 fs. We also show that a grating system can run for hours at 10 Hz without degradation. The contrast improvement from an ionization grating compares favorably to that achievable with plasma mirrors., Comment: 6 pages, 4 figures

High-spin molecules allow for bottom-up qubit design and are promising platforms for magnetic sensing and quantum information science. Optical addressability of molecular electron spins has also been proposed in first-row transition metal complexes via optically-detected magnetic resonance (ODMR) mechanisms analogous to the diamond-NV colour centre. However, significantly less progress has been made on the front of metal-free molecules, which can deliver lower costs and milder environmental impacts. At present, most luminescent open-shell organic molecules are $\pi$-diradicals, but such systems often suffer from poor ground-state open-shell characters necessary to realise a stable ground-state molecular qubit. In this work, we use alternancy symmetry to selectively minimise radical-radical interactions in the ground state, generating $\pi$-systems with high diradical characters. We call them m-dimers, referencing the need to covalently link two benzylic radicals at their meta carbon atoms for the desired symmetry. Through a detailed electronic structure analysis, we find that the excited states of alternant hydrocarbon m-diradicals contain important symmetries that can be used to construct ODMR mechanisms leading to ground-state spin polarisation. The molecular parameters are set in the context of a tris(2,4,6-trichlorophenyl)methyl (TTM) radical dimer covalently tethered at the meta position, demonstrating the feasibility of alternant m-diradicals as molecular colour centres., Comment: 12 pages, 5 figures, 1 table. Minor edits made to the manuscript text

In this paper we discuss the principles of measuring topological charge or representation traveling in the set of anyons. We describe the procedure and analyze how it works for the different values of parameters of the theory. We also show how it can be modified to be more effective for different levels of Chern-Simons theory., Comment: 6 pages, 5 figures

Beam-beam interactions pose substantial challenges in the design and operation of circular colliders, significantly affecting their performance. In particular, the weak-strong simulation approach is pivotal for investigating single-particle dynamics during the collider design phase. This paper evaluates the limitations of existing models in weak-strong simulations, noting that while they accurately account for energy changes due to slingshot effects, they fail to incorporate longitudinal coordinate changes ($z$-variation). To address this gap, we introduce two novel transformations that enhance Hirata's original framework by including both $z$-variation and slingshot effect-induced energy changes. Through rigorous mathematical analysis and extensive weak-strong simulation studies, we validate the efficacy of these enhancements in achieving a more precise simulation of beam-beam interactions. Our results reveal that although $z$-variation constitutes a higher-order effect and does not substantially affect the emittance growth rate within the specific design parameters of the Electron-Ion Collider (EIC), the refined model offers improved accuracy, particularly in scenarios involving the interaction between beam-beam effects and other random diffusion processes, as well as in simulations incorporating realistic lattice models., Comment: 11 pages, 4 figures