The $\textrm{HRI}_\textrm{EUV}$ telescope was calibrated on ground at the Physikalisch-Technische Bundesanstalt (PTB), Germany's national metrology institute, using the Metrology Light Source (MLS) synchrotron in April 2017 during the calibration campaign of the Extreme Ultraviolet Imager (EUI) instrument onboard the Solar Orbiter mission. We use the pre-flight end-to-end calibration and component-level (mirror multilayer coatings, filters, detector) characterization results to establish the beginning-of-life performance of the $\textrm{HRI}_\textrm{EUV}$ telescope which shall serve as a reference for radiometric analysis and monitoring of the telescope in-flight degradation. Calibration activities at component level and end-to-end calibration of the instrument were performed at PTB/MLS synchrotron light source (Berlin, Germany) and the SOLEIL synchrotron. Each component optical property is measured and compared to its semi-empirical model. This pre-flight characterization is used to estimate the parameters of the semi-empirical models. The end-to-end response is measured and validated by comparison with calibration measurements, as well as with its main design performance requirements. The telescope spectral response semi-empirical model is validated by the pre-flight end-to-end ground calibration of the instrument. It is found that $\textrm{HRI}_\textrm{EUV}$ is a highly efficient solar EUV telescope with a peak efficiency superior to 1 e$^-$.ph$^{-1}$), low detector noise ($\approx$ 3 e- rms), low dark current at operating temperature, and a pixel saturation above 120 ke- in low-gain or combined image mode. The ground calibration also confirms a well-modeled spectral selectivity and rejection, and low stray light. The EUI instrument achieves state-of-the-art performance in terms of signal-to-noise and image spatial resolution.

David Bohm has put forward the first deterministic interpretation of quantum physics, and for this he seems to be regarded as a champion of determinism by physicists (both his contemporaries and the supporters of his interpretation, the so-called "Bohmians") as well as by historians of physics. The standard narrative is that he underwent a "conversion" from being a supporter of Bohr to being a staunch determinist, due to his interaction with Einstein and his commitment to Marxism. Here we show that Bohm actually upheld with continuity throughout his career some philosophical tenets that included a strong rejection of mechanistic determinism. As such, we conclude that Bohm was never a Bohmian and that his philosophical views have been largely misinterpreted.

Orthogonal Time Frequency Space (OTFS) systems face significant challenges in channel estimation due to high pilot overhead and peak-to-average power ratio (PAPR). To address these issues, we propose a two-step channel estimation method for Zero-Pad OTFS (ZP-OTFS), a modified OTFS system characterized by multiple zero rows along the delay axis. This method strategically inserts pilot sequences into the zero bins of the ZP-OTFS system, effectively mitigating overhead and PAPR. Comprehensive simulation results validate the effectiveness of our proposed method, demonstrating its superior performance over traditional embedded pilot estimation in high Signal-to-Noise Ratio (SNR) scenarios. Specifically, our method achieves a lower normalized mean square error (NMSE) and better bit error rates (BER) at high SNRs.

Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum computing. This work stresses that for translationally invariant lattice Hamiltonians with periodic boundary conditions, one can easily derive efficiently computable lower bounds to ground state energies that can and should be compared with variational principles providing upper bounds. As small technical results, it is shown that (i) the Anderson bound and a (ii) common hierarchy of semi-definite relaxations both provide approximations with performance guarantees that scale like a constant in the energy density for cubic lattices. (iii) Also, the Anderson bound is systematically improved as a hierarchy of semi-definite relaxations inspired by the quantum marginal problem.

Orthogonal time frequency space (OTFS) technique is a two-dimensional modulation method that multiplexes information symbols in the delay-Doppler (DD) domain. OTFS combats high Doppler shift existing in high speed wireless communication. However, conventional channel estimation in OTFS suffers from high pilot overhead because guard symbols occupy a significant part of the DD domain grids. In this paper, a superimposed channel estimation is proposed which can completely estimate channel parameters without considering pilot overhead and performance degradation. As the channel state information (CSI) in the DD domain is sparse, a sparse recovery algorithm orthogonal matching pursuit (OMP) is used. Besides, our proposed method does not suffer from high peak to average power ratio (PAPR). To detect information symbols, a message passing (MP) detector, which exploits the sparsity of DD channel representation, is employed.

Proton therapy is an emerging method in cancer therapy. One of the main developments is to increase the accuracy of the Bragg-peak position calculation, which requires more precise relative stopping power (RSP) measurements. A promising choice is the application of proton computed tomography (pCT) systems which takes the images under similar conditions, as they use the same irradiation device and hadron beam for imaging and treatment. A key aim is to develop a precise image reconstruction algorithm for pCT systems to reach their maximal performance. In this work, an iterative image reconstruction algorithm, based on the Richardson-Lucy iteration is proposed for the first time for proton CT image reconstruction. Monte Carlo (MC) simulations of CTP528 and CTP404 phantoms were used to benchmark the proposed method. In the case of an idealized detector setup, using a 1 mm pitch grid, 4.88 lp/cm spatial resolution and 0.66% average RSP uncertainty was achieved. The present method provides a promising proof-of-concept candidate for compromise between accuracy and speed with several further development directions.

The modular group PSL(2;Z) acts on the hyperbolic plane HP with quotient the modular surface M, whose unit tangent bundle U is a 3-manifold homeomorphic to the complement of the trefoil knot in the 3-sphere. The hyperbolic conjugacy classes of PSL(2;Z) correspond to the closed oriented geodesics in M. Those lift to the periodic orbits for the geodesic flow in U, which define the modular knots. The linking numbers between modular knots and the trefoil is well understood. Indeed, Etienne Ghys showed in 2006 that they are given by the Rademacher invariant of the corresponding conjugacy classes. The Rademacher function is a homogeneous quasi-morphism of PSL(2;Z) which he had recognised with Jean Barge in 1992 as half the primitive of the bounded euler class. This shed light on the 1987 work of Michael Atiyah concerning the logarithm of the Dedekind eta function which identified it with no less than that six other important functions appearing in diverse areas of mathematics. We are concerned with the linking numbers between modular knots and derive several formulae with arithmetical, combinatorial, topological and group theoretical flavours. In particular we associate to a pair of modular knots a function defined on the character variety of PSL(2;Z), whose limit at the boundary point recovers their linking number. Moreover, we show that the linking number with a modular knot minus that with its inverse yields a homogeneous quasi-morphism on the modular group, and how to extract a free basis out of these. For this we prove that the linking pairing is non degenerate.

We study the $n^{\rm th}$ centered moments of the $1$-level density for the low-lying zeros of $L$-functions attached to holomorphic cuspidal newforms of large prime level and fixed weight. Assuming the Generalized Riemann Hypotheses, we compute this statistic for any $n\ge 1$ and for all test functions whose Fourier transforms are supported in $\left(-2/n, \, 2/n\right)$. This is believed to be the natural limit of the current technology. Our work significantly extends beyond the trivial range $(-1/n, \, 1/n)$ and surpasses the previous record of $(-1/(n-1),\, 1/(n-1))$ whenever $n>2$. The Katz-Sarnak philosophy predicts that the aforementioned statistic can be modeled by the corresponding statistic for the eigenvalues of random orthogonal matrices. We prove that this is the case for test functions with Fourier support contained in $(-2/n,\, 2/n)$. The main technical innovation is a tractable vantage to evaluate the combinatorial zoo of terms, similar to the work of Conrey-Snaith and Mason-Snaith. As an application, our work provides better bounds on the order of vanishing at the central point for the $L$-functions in our family.

Extending the work of the first author, we introduce a notion of semisimple topological field theory in arbitrary even dimension and show that such field theories necessarily lead to stable diffeomorphism invariants. The main result of this paper is a proof that this 'upper bound' is optimal: To this end, we introduce and study a class of `finite path integral' topological field theories which are semisimple and which generalize well known theories constructed by Dijkgraaf-Witten, Freed and Quinn. We show that manifolds satisfying a certain finiteness condition -- including 4-manifolds with finite fundamental group -- are indistinguishable to these field theories if and only if they are stably diffeomorphic. Subject to these finiteness conditions, such finite path integral theories therefore provide the strongest semisimple TFT invariants possible. These results hold for a large class of ambient tangential structures. We discuss a number of applications, including the constructions of unoriented 4-dimensional semisimple field theories which can distinguish unoriented smooth structure and oriented higher-dimensional semisimple field theories which can distinguish certain exotic spheres. Along the way, we show that dimensional reductions of finite path integral theories are again finite path integral theories, we utilize ambidexterity in the rational setting, and we develop techniques related to the $\infty$-categorical Möbius inversion principle of Gálvez-Carrillo--Kock--Tonks.

We show that the axiom of choice, a basic yet controversial postulate of set theory, leads to revise the standard understanding of one of the pillars of our best physical theories, namely the no-signaling principle. While it is well known that probabilistic no-signaling resources (such as quantum non-locality) are stronger than deterministic ones, we show-by invoking the axiom of choice-the opposite: Functional (deterministic) no-signaling resources can be stronger than probabilistic ones. To prove this, we devise a Bell-like game that shows a systematic advantage of functional no-signaling with respect to any probabilistic no-signaling resource.

We present ETCetera, a Python library developed for the analysis and synthesis of the sampling behaviour of event triggered control (ETC) systems. In particular, the tool constructs abstractions of the sampling behaviour of given ETC systems, in the form of timed automata (TA) or finite-state transition systems (FSTSs). When the abstraction is an FSTS, ETCetera provides diverse manipulation tools for analysis of ETC's sampling performance, synthesis of communication traffic schedulers (when networks shared by multiple ETC loops are considered), and optimization of sampling strategies. Additionally, the TA models may be exported to UPPAAL for analysis and synthesis of schedulers. Several examples of the tool's application for analysis and synthesis problems with different types of dynamics and event-triggered implementations are provided.

We prove that Real topological Hochschild homology can be characterized as the norm from the cyclic group of order $2$ to the orthogonal group $O(2)$. From this perspective, we then prove a multiplicative double coset formula for the restriction of this norm to dihedral groups of order $2m$. This informs our new definition of Real Hochschild homology of rings with anti-involution, which we show is the algebraic analogue of Real topological Hochschild homology. Using extra structure on Real Hochschild homology, we define a new theory of $p$-typical Witt vectors of rings with anti-involution. We end with an explicit computation of the degree zero $D_{2m}$-Mackey functor homotopy groups of $\operatorname{THR}(\underline{\mathbb{Z}})$ for $m$ odd. This uses a Tambara reciprocity formula for sums for general finite groups, which may be of independent interest.

We show that fully-localized, three-dimensional, time-reversal-symmetry-broken insulators do not belong to a single phase of matter but can realize topologically distinct phases that are labelled by integers. The phase transition occurs only when the system becomes conducting at some filling. We find that these novel topological phases are fundamentally distinct from insulators without disorder: they are guaranteed to host delocalized boundary states giving rise to the quantized boundary Hall conductance, whose value is equal to the bulk topological invariant.

We prove that every slightly degenerate braided fusion category admits a minimal nondegenerate extension, and hence that every pseudo-unitary super modular tensor category admits a minimal modular extension. This completes the program of characterizing minimal nondegenerate extensions of braided fusion categories. Our proof relies on the new subject of fusion 2-categories. We study in detail the Drinfel'd centre Z(Mod-B) of the fusion 2-category Mod-B of module categories of a braided fusion 1-category B. We show that minimal nondegenerate extensions of B correspond to certain trivializations of Z(Mod-B). In the slightly degenerate case, such trivializations are obstructed by a class in $\mathrm{H}^5(K(\mathbb{Z}_2, 2); k^\times)$ and we use a numerical invariant -- defined by evaluating a certain two-dimensional topological field theory on a Klein bottle -- to prove that this obstruction always vanishes. Along the way, we develop techniques to explicitly compute in braided fusion 2-categories which we expect will be of independent interest. In addition to the model of Z(Mod-B) in terms of braided B-module categories, we develop a computationally useful model in terms of certain algebra objects in B. We construct an S-matrix pairing for any braided fusion 2-category, and show that it is nondegenerate for Z(Mod-B). As a corollary, we identify components of Z(Mod-B) with blocks in the annular category of B and with the homomorphisms from the Grothendieck ring of the Müger centre of B to the ground field.

The advent of multi-messenger astronomy has allowed for new types of source searches by neutrino detectors. We present the results of the search for 0.5-100 GeV astrophysical neutrinos detected with IceCube and emitted from compact binary mergers detected by the LIGO, Virgo, and KAGRA interferometers from their first run of observation (O1) to the end of the first part of the fourth (O4a). An innovative approach is used to lower the energy threshold to 0.5 GeV and to search for an excess of GeV neutrinos in time coincidence with astrophysical transient events. Furthermore, we use a statistical combination of all observations, a binomial test, to search for a subpopulation of neutrino emitters. No significant excess was found from the studied mergers, with a best post-trial $p$-value of $40\%$, and there is currently no hint of a population of GeV neutrino emitters found in the IceCube data (post-trial $p$-value = $81\%$).

The representation dimension of a finite group $G$ is the minimal dimension of a faithful complex linear representation of $G$. We prove that the representation dimension of any finite group $G$ is at most $\sqrt{|G|}$ except if $G$ is a $2$-group with elementary abelian center of order $8$ and all irreducible characters of $G$ whose kernel does not contain $Z(G)$ are fully ramified with respect to $G/Z(G)$. We also obtain bounds for the representation dimension of quotients of $G$ in terms of the representation dimension of $G$, and discuss the relation of this invariant with the essential dimension of $G$.

Let G be a finite group, Irr(G) the set of all irreducible complex characters of G and X \in Irr(G). Let also cod(X) = |G : kerX|/X(1) and cod(G) = {cod(X) | X \in Irr(G)}. In this note, we show that the simple group PSL(2, q), for a prime power q > 3, is uniquely determined by the set of its codegree.

A braided monoidal category may be considered a $3$-category with one object and one $1$-morphism. In this paper, we show that, more generally, $3$-categories with one object and $1$-morphisms given by elements of a group $G$ correspond to $G$-crossed braided categories, certain mathematical structures which have emerged as important invariants of low-dimensional quantum field theories. More precisely, we show that the 4-category of $3$-categories $\mathcal{C}$ equipped with a 3-functor $\mathrm{B}G \to \mathcal{C}$ which is essentially surjective on objects and $1$-morphisms is equivalent to the $2$-category of $G$-crossed braided categories. This provides a uniform approach to various constructions of $G$-crossed braided categories.

The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant descriptions of the models within the Lagrangian and Hamiltonian formalisms with constraints are proposed. It is shown that the models are de Sitter-invariant and integrable. An explicit solution of equations of motion is derived in quadratures by means of projection operator technique.

We prove that semisimple 4-dimensional oriented topological field theories lead to stable diffeomorphism invariants and can therefore not distinguish homeomorphic closed oriented smooth 4-manifolds and homotopy equivalent simply connected closed oriented smooth 4-manifolds. We show that all currently known 4-dimensional field theories are semisimple, including unitary field theories, and once-extended field theories which assign algebras or linear categories to 2-manifolds. As an application, we compute the value of a semisimple field theory on a simply connected closed oriented 4-manifold in terms of its Euler characteristic and signature. Moreover, we show that a semisimple 4-dimensional field theory is invariant under $\mathbb{C}P^2$-stable diffeomorphisms if and only if the Gluck twist acts trivially. This may be interpreted as the absence of fermions amongst the `point particles' of the field theory. Such fermion-free field theories cannot distinguish homotopy equivalent 4-manifolds. Throughout, we illustrate our results with the Crane-Yetter-Kauffman field theory associated to a ribbon fusion category. As an algebraic corollary of our results applied to this field theory, we show that a ribbon fusion category contains a fermionic object if and only if its Gauss sums vanish.

Let a reductive group $G$ act on a smooth variety $X$ such that a good quotient $X{/\!\!/}G$ exists. We show that the derived category of a noncommutative crepant resolution (NCCR) of $X{/\!\!/} G$, obtained from a $G$-equivariant vector bundle on $X$, can be embedded in the derived category of the (canonical, stacky) Kirwan resolution of $X{/\!\!/} G$. In fact the embedding can be completed to a semi-orthogonal decomposition in which the other parts are all derived categories of Azumaya algebras over smooth Deligne-Mumford stacks.

A framework is proposed that addresses both conditional density estimation and latent variable discovery. The objective function maximizes explanation of variability in the data, achieved through the optimal transport barycenter generalized to a collection of conditional distributions indexed by a covariate --either given or latent-- in any suitable space. Theoretical results establish the existence of barycenters, a minimax formulation of optimal transport maps, and a general characterization of variability via the optimal transport cost. This framework leads to a family of non-parametric neural network-based algorithms, the BaryNet, with a supervised version that estimates conditional distributions and an unsupervised version that assigns latent variables. The efficacy of BaryNets is demonstrated by tests on both artificial and real-world data sets. A parallel drawn between autoencoders and the barycenter framework leads to the Barycentric autoencoder algorithm (BAE).

Bayesian methods are often optimal, yet increasing pressure for fast computations, especially with streaming data, brings renewed interest in faster, possibly sub-optimal, solutions. The extent to which these algorithms approximate Bayesian solutions is a question of interest, but often unanswered. We propose a methodology to address this question in predictive settings, when the algorithm can be reinterpreted as a probabilistic predictive rule. We specifically develop the proposed methodology for a recursive procedure for online learning in nonparametric mixture models, often refereed to as Newton's algorithm. This algorithm is simple and fast; however, its approximation properties are unclear. By reinterpreting it as a predictive rule, we can show that it underlies a statistical model which is, asymptotically, a Bayesian, exchangeable mixture model. In this sense, the recursive rule provides a quasi-Bayes solution. While the algorithm only offers a point estimate, our clean statistical formulation allows us to provide the asymptotic posterior distribution and asymptotic credible intervals for the mixing distribution. Moreover, it gives insights for tuning the parameters, as we illustrate in simulation studies, and paves the way to extensions in various directions. Beyond mixture models, our approach can be applied to other predictive algorithms.

The clustering problem, and more generally, latent factor discovery --or latent space inference-- is formulated in terms of the Wasserstein barycenter problem from optimal transport. The objective proposed is the maximization of the variability attributable to class, further characterized as the minimization of the variance of the Wasserstein barycenter. Existing theory, which constrains the transport maps to rigid translations, is extended to affine transformations. The resulting non-parametric clustering algorithms include k-means as a special case and exhibit more robust performance. A continuous version of these algorithms discovers continuous latent variables and generalizes principal curves. The strength of these algorithms is demonstrated by tests on both artificial and real-world data sets.

The article is devoted to the expansion of iterated Stratonovich stochastic integrals of second multiplicity into the double series of products of standard Gaussian random variables. The proof of expansion is based on the application of double Fourier-Legendre series and double trigonometric Fourier series summarized by Pringsheim method. The results of the article are generalized to the case of an arbitrary complete orthonormal system of functions in the space $L_2([t, T])$ and $ψ_1(τ), ψ_2(τ)\in L_2([t, T]).$ The considered expansion can be applied to the numerical integration of Ito stochastic differential equations. Some recent results on the expansion of iterated Stratonovich stochastic integrals of multiplicities 3 to 6 are given.

For $G$ a symplectic or orthogonal $p$-adic group (not necessarily split), or an inner form of a general linear $p$-adic group, we compute the endomorphism algebras of some induced projective generators à la Bernstein of the category of smooth representations of $G$ and show that these algebras are isomorphic to the semi-direct product of a Hecke algebra with parameters by a finite group algebra. Our strategy and parts of our intermediate results apply to a general reductive connected $p$-adic group.

Decoding the self-assembly mechanism of metal-organic frameworks is a crucial step in reducing trial-and-error tests in their synthesis protocols. Atomistic simulations have proven essential in revealing molecular-level features of MOF nucleation, but they still exhibit limitations in the simulation setups due to size constraints (inability of reaching realistic concentrations or exploring non-stoichiometric metal:ligand ratios). In this contribution, we develop a methodology to derive reactive coarse grained force fields based on multiscale coarse graining methods. We apply our novel methodology to the case of the archetypal zeolitic-imidazolate framework ZIF-8. Our coarse grained force field, which we call nb-CG-ZIF-FF, does not contain any explicit connectivity information, but learns the tetrahedral Zn-connectivity from many body correlations within an atomistic benchmark. nb-CG-ZIF-FF quantitatively reproduces the features of bulk, crystalline ZIF-8 as well as the structural evolution of pre-nucleation species in terms of Zn n-fold coordination populations from the atomistic benchmark. While the range of rings that are formed along the synthesis process are well captured by nb-CG-ZIF-FF, the model cannot exactly reproduce ring populations. Our reactive CG force field fitting approach can be applied to any MOF, opening new research avenues in modeling MOF formation, decomposition, defect dynamics and phase transition processes.

This paper addresses the problem of adaptive codebook (CB) selection for downlink (DL) precoder quantization in channel state information (CSI) reporting. The accuracy of precoder quantization depends on propagation conditions, requiring independent parameter adaptation for each user equipment (UE). To enable optimal CB selection, this paper proposes UE-assisted CB selection at the base station (BS) using reported by the UE statistical channel properties across time, frequency, and spatial domains. The reported assistance information serves as input to a neural network (NN), which predicts the quantization accuracy of various CB types for each served user. The predicted accuracy is then used to select the optimal CB while considering the associated CSI reporting overhead and precoding performance. System-level simulations demonstrate that the proposed approach reduces total CSI overhead while maintaining the target system throughput performance.

We prove that a local $L^p(V_2)$ variation norm estimate fails for circular means in two dimensions, and quantify this failure by proving lower bounds for functions of exponential type. This is related to lower bounds for Fourier multipliers supported on annuli, of the type considered by Córdoba.

Non-trivial spatial topology of the Universe can imprint potentially observable signatures on the cosmic microwave background (CMB). In this study, we investigate how deviations from the standard nearly-scale-free primordial power spectrum impact observables for the fully compact, orientable Euclidean topologies ($E_1$--$E_6$). We examine how such deviations modify the detectability of the underlying topology, depending on whether they are an intrinsic consequence of non-trivial topology or independent of it. We compute CMB temperature correlation matrices across a range of topologies, fundamental domain sizes, and observer locations for both standard and modified primordial power spectra. The impact of these modifications on the detectability of topology is quantified using the Kullback-Leibler divergence, providing an estimate of the distinguishability of non-trivial and simply-connected topologies based solely on CMB temperature observations. In addition, we employ the CatBoost machine learning algorithm to classify harmonic-space realizations of CMB temperature maps and thereby assess the observational prospects for topology detection. Signatures of non-trivial topology are encoded in the off-diagonal structure of the CMB temperature correlation matrices and are most prominent on the largest angular scales. Deviations from the simple power-law primordial spectrum at these scales can substantially alter the detectability of topology, either enhancing its characteristic CMB imprints or suppressing them below observational sensitivity. Our results demonstrate that uncertainties in the primordial power spectrum must be carefully accounted for in robust searches for cosmic topology using the CMB.