Unitary transformations are employed to enhance the violations of the Bell-CHSH inequality in relativistic Quantum Field Theory. The case of the scalar field in $1+1$ Minkowski space-time is scrutinized by relying on the Tomita-Takesaki modular theory. The example of the bounded Hermitian operator $sign(φ(f))$, where $φ(f)$ stands for the smeared scalar field, is worked out. It is shown that unitary deformations enable for violations of the Bell-CHSH inequality. The setup is generalized to the Proca vector field by means of its equivalence with the scalar theory.

Background: Type I X-Ray bursts (XRBs) are energetic stellar explosions that occur on the surface of a neutron star in an accreting binary system with a low-mass H/He-rich companion. The rate of the $^{34}$Ar($α,p$)$^{37}$K reaction may influence features of the light curve that results from the underlying thermonuclear runaway, as shown in recent XRB stellar modelling studies. Purpose: In order to reduce the uncertainty of the rate of this reaction, properties of resonances in the compound nucleus $^{38}$Ca, such as resonance energies, spins, and particle widths, must be well constrained. Method: This work discusses a study of resonances in the $^{38}$Ca compound nucleus produced in the $^{34}$Ar($α,p$) reaction. The experiment was performed at the National Superconducting Cyclotron Laboratory, with the ReA3 facility by measuring proton scattering using an unstable $^{37}$K beam. The kinematics were designed specifically to identify and characterize resonances in the Gamow energy window for the temperature regime relevant to XRBs. Results: The spins and proton widths of newly identified and previously known states in $^{38}$Ca in the energy region of interest for the $^{34}$Ar($α,p$)$^{37}$K reaction have been constrained through an R-Matrix analysis of the scattering data. Conclusions: Using these constraints, a newly estimated rate is applied to an XRB model built using Modules for Experiments in Stellar Astrophysics (MESA), to examine its impact on observables, including the light curve. It is found that the newly determined reaction rate does not substantially affect the features of the light curve.

Water confined to channels one nanometer thick exhibits electrochemical behavior distinct from bulk water, including enhanced protonic conductivity and large dielectric anisotropy. Here, we exploit these characteristics to design a scalable electrochemical energy-storage system ("blue capacitor") constructed entirely from naturally abundant materials. By assembling layered clays and conductive graphene, we produce 1-nm-thick channels in which confined water acts as the sole electrolyte. We systematically study different clay types, the electrode composition, and separator thickness using complementary physicochemical and electrochemical techniques. The device operates stably up to 1.6 V, achieves specific capacitances of up to 40 F/g, nearly 100% coulombic efficiency, and stable performance over more than 60,000 charge-discharge cycles. Structural and dynamic analyses validate the device architecture, water purity, and proton transport in the nanopores. These results demonstrate that nanoconfined water can function as an electrolyte in a macroscopic electrochemical device, providing a platform for exploring sustainable aqueous energy-storage systems.

The increasing availability of multiple network data has highlighted the need for statistical models for heterogeneous populations of networks. A convenient framework makes use of metrics to measure similarity between networks. In this context, we propose a novel Bayesian nonparametric model that identifies clusters of networks characterized by similar connectivity patterns. Our approach relies on a location-scale Dirichlet process mixture of centered Erdős--Rényi kernels, with components parametrized by a unique network representative, or mode, and a univariate measure of dispersion around the mode. We demonstrate that this model has full support in the Kullback--Leibler sense and is strongly consistent. An efficient Markov chain Monte Carlo scheme is proposed for posterior inference and clustering of multiple network data. The performance of the model is validated through extensive simulation studies, showing improvements over state-of-the-art methods. Additionally, we present an effective strategy to extend the application of the proposed model to datasets with a large number of nodes. We illustrate our approach with the analysis of human brain network data.

We present a workflow that iteratively combines \textit{ab-initio} calculations with a machine-learning (ML) guided search for superconducting compounds with both dynamical stability and instability from imaginary phonon modes, the latter of which have been largely overlooked in previous studies. Electron-phonon coupling (EPC) properties and critical temperature (T$_c$) of 417 boron, carbon, and borocarbide compounds have been calculated with density functional perturbation theory (DFPT) and isotropic Eliashberg approximation. Our study addresses T$_c$ convergence of Brillouin zone sampling with an ansatz test, stabilizing imaginary phonon modes for significant EPC contributions and comparing performance of two ML models especially when including compounds of dynamical instability. We predict a few promising superconducting compounds with formation energy just above the ground state convex hull, such as Ca$_5$B$_3$N$_6$ (35 K), TaNbC$_2$ (28.4 K), Nb$_3$B$_3$C (16.4 K), Y$_2$B$_3$C$_2$ (4.0 K), Pd$_3$CaB (7.0 K), MoRuB$_2$ (15.6 K), RuVB$_2$ (15.0 K), RuSc$_3$C$_4$ (6.6 K) among others.

Shannon entropy, as a chaos indicator, is used for online Poincaré map regularization and dynamic aperture optimization in the National Synchrotron Light Source-II (NSLS-II) ring. Although various chaos indicators are widely used in studying nonlinear dynamical systems, including modern particle accelerators, it is the first time to use a measurable one in a real-world machine for online nonlinear optimization. Poincaré maps, constructed with the turn-by-turn beam trajectory readings from beam position monitors, are commonly used to observe the nonlinearity in ring-based accelerators. However, such observations typically only provide a qualitative interpretation. We analyze their entropy to quantify the chaos in measured Poincaré maps. After some canonical transformations on the Poincaré maps, not only can the commonly used nonlinear characterizations be extracted, but more importantly, the chaos can be quantitatively calibrated with Shannon entropy, and then used as the online optimization objectives.

This paper reports recent lattice characterization results obtained at the National Synchrotron Light Source II (NSLS-II) storage ring, conducted without reliance on a lattice model. A pair of beam position monitors (BPMs) with bunch-by-bunch (B$\times$B) resolution, were recently installed in a section of the storage ring free of magnetic fields. The new BPM pair measured the beam, or bunch's transverse Poincaré map precisely after the beam was excited. Linear one-turn-matrices (OTM) were then derived, and from these, the 4-dimensional coupled Twiss parameters were extracted at the locations of the BPM pair. By normalizing beam oscillation amplitudes with the Twiss parameters, the global action-variables were obtained. These action-variables facilitated the measurement of the local Twiss parameters observed by other BPMs independent on lattice model. This method is general, and particularly useful in certain scenarios such as a round beam mode in a diffraction-limited light source ring. We applied it to assess both weakly and strongly coupled lattices at the NSLS-II ring. Through analysis of the strongly coupled lattice, the quadrupole tilt errors were estimated to be less than 400 \siμrad. Utilizing the BPMs' B$\times$B resolution, for the first time we observed the variations of the linear lattice along a long bunch-train.

The classic theorem of Gallai and Milgram (1960) generalizes several fundamental results in Graph Theory, such as Dilworth's theorem on posets and Kőnig's theorem on matchings in bipartite graphs. The theorem asserts that for every graph G, the vertex set of G can be partitioned into at most α(G) vertex-disjoint paths, where α(G) is the maximum size of an independent set in G. The proof of the Gallai-Milgram theorem is constructive and yields a polynomial-time algorithm that computes a covering of G by at most α(G) vertex-disjoint paths. While the Gallai-Milgram theorem is tight, it was not known prior to our work whether deciding if a graph G could be covered by fewer than α(G) vertex-disjoint paths can be done in polynomial time. We resolve this question by proving the following algorithmic extension of the Gallai-Milgram theorem for undirected graphs: There is an algorithm that, for an n-vertex graph G and an integer parameter k \ge 1, runs in time 2^{2^{O(k^4\log{k})}} \cdot n^{O(1)} and outputs a path cover P of G together with - a correct conclusion that P is a minimum-size path cover, or - an independent set of size |P|+k, certifying that P contains at most α(G) - k paths. The proof of our algorithmic extension of the Gallai-Milgram theorem is non-trivial and builds on several novel algorithmic ideas. One of the key subroutines in our algorithm is an FPT algorithm, parameterized by α(G), for deciding whether G contains a Hamiltonian path. This result is of independent interest - prior to our work no polynomial-time algorithm for deciding Hamiltonicity was known even for graphs with independence number at most three. Moreover, the algorithmic techniques we develop apply to a wide array of problems in undirected graphs, including Hamiltonian Cycle, Path Cover, Largest Linkage, and Topological Minor Containment.

In this paper, we apply approximate entropy (ApEn) analysis to the nonlinear beam dynamics in circular accelerators. Due to the presence of strong nonlinear magnets, chaos of beam motion gradually increases with amplitude. Such chaos can be quantitatively characterized with ApEn of beam turn-by-turn readings. Then ApEn, as a chaos indicator, can be used for nonlinear lattice optimization and analysis.

In this note we elaborate on some notions of surface area for discrete graphs which are closely related to the inverse degree. These notions then naturally lead to associated connectivity measures of graphs and to the definition of a special class of large graphs, called social graphs, that might prove interesting for applications. In addition, we derive spectral estimates involving the surface area and, as a main result, present an upper bound on the second eigenvalue for planar graphs which in some cases improves upon existing bounds from D. A. Spielman and S.-H. Teng, Spectral partitioning works: Planar graphs and finite element meshes, and M. Plümer, Upper eigenvalue bounds for the Kirchhoff Laplacian on embedded metric graphs.

Many hypergeometric differential systems that arise from a geometric setting can be endowed with the structure of mixed Hodge modules. We generalize this fundamental result to the tautological systems associated to homogeneous spaces by giving a functorial construction for them. As an application, we solve the holonomic rank problem for such tautological systems in full generality.

Information theory, though originally developed for communications engineering, provides mathematical tools with broad applications across science. These tools characterize the fundamental limits of data compression and transmission in the presence of noise. Here, we present a visual, intuition-driven guide to key concepts in information theory. We show how entropy, mutual information, and channel capacity follow from basic probability, and how they determine the shortest possible encoding of a data source and the maximum rate of reliable communication through a noisy channel. Our presentation assumes only a familiarity with basic probability theory.

For some synchrotron light source beamline applications, a round beam is preferable to a flat one. A conventional method of obtaining round beam in an electron storage ring is to shift its tune close to a linear difference resonance. The linearly coupled beam dynamics is analyzed with perturbation theories, which have certain limitations. In this paper, we adopt the Solution by LInear Matrices (SLIM) analysis to calculate exact beam sizes to design round beam lattices. The SLIM analysis can deal with a generally linearly coupled accelerator lattice. The effects of various coupling sources on beam emittances and sizes can be studied within a self-consistent frame. Both the on- and off-resonance schemes to obtain round beams are explained with examples. The SLIM formalism for two widely used magnet models: combined-function bending magnets, and planar wigglers and undulators, is also derived.

We consider the problem of identifying a mixture of Gaussian distributions with same unknown covariance matrix by their sequence of moments up to certain order. Our approach rests on studying the moment varieties obtained by taking special secants to the Gaussian moment varieties, defined by their natural polynomial parametrization in terms of the model parameters. When the order of the moments is at most three, we prove an analogue of the Alexander-Hirschowitz theorem classifying all cases of homoscedastic Gaussian mixtures that produce defective moment varieties. As a consequence, identifiability is determined when the number of mixed distributions is smaller than the dimension of the space. In the two component setting we provide a closed form solution for parameter recovery based on moments up to order four, while in the one dimensional case we interpret the rank estimation problem in terms of secant varieties of rational normal curves.

We study the autocovariance functions of moving average random fields over the integer lattice $\mathbb{Z}^d$ from an algebraic perspective. These autocovariances are parametrized polynomially by the moving average coefficients, hence tracing out algebraic varieties. We derive dimension and degree of these varieties and we use their algebraic properties to obtain statistical consequences such as identifiability of model parameters. We connect the problem of parameter estimation to the algebraic invariants known as euclidean distance degree and maximum likelihood degree. Throughout, we illustrate the results with concrete examples. In our computations we use tools from commutative algebra and numerical algebraic geometry.

We obtain rigorous a priori upper and lower bounds to the exact period of the celebrated Rayleigh stretched string differential equation. We use them to show that Rayleigh's approximative period overestimates the true period and that the relative error is, to a first approximation, directly proportional to the initial fractional displacement and inversely proportional to the initial stretch. Thus, for a given length and stretch, one can determine the initial displacement so as to guarantee a prescribed accuracy in Rayleigh's period while for a given displacement one can see why the relative error blows up of the initial stretch is tiny. We have replaced the big-O terms with explicit inequalities and a new elegant formula for the relative error.

R. Heitmann's proof of the Direct Summand Conjecture has opened a new approach to the study of homological conjectures in mixed characteristic. Inspired by his work and by the methods of almost ring theory, we discuss a normalized length for certain torsion modules, which was introduced by G. Faltings. Using the normalized length and the Frobenius map, we prove some results of local cohomology for local rings in mixed characteristic, which has an immediate implication for the subject of splinters studied by A. Singh.

A covariant quantization of type IIB and type IIA superparticles in their spinor moving frame formulation reveals the hidden $SU(8)$ symmetry of the linearized type II supergravity. It acts on auxiliary variables parameterizing the possible choices of complex structures which is necessary to arrive at the realization of the quantum state vector as an analytic on-shell superfield, the one-particle counterpart of analytical superamplitudes for type IIB and type IIA supergravity multiplets. The description of the type IIA supergraity multiplet in terms of an analytic on-shell superfield is then identical to that for type IIB supermultiplet; the difference is in spacetime interpretation. However, the definition of suitable auxiliary variables in type IIA case requires introduction of covariantly constant $SO(8)$ vector which can be related to T-duality transform between type IIA and type IIB superspaces. The simplest analytic IIB superamplitudes discussed in the literature thus also describe type IIA processes. We elaborate on these using the spinor moving frame (Lorentz harmonic) formalism and point out the restrictions on computation of many particle type IIA amplitudes in this approach. We also briefly discuss the initial steps towards type IIA superamplitudes involving, besides supergravity multiplets, also D$0$-branes (Dirichlet superparticles), which was recently quantized in the similar formalism, and indicate some problems which appear are to be solved to proceed on this way.

The transversal rank of a hypergraph is the maximum size of its minimal hitting sets. Deciding, for an $n$-vertex, $m$-edge hypergraph and an integer $k$, whether the transversal rank is at least $k$ takes time $O(m^{k+1} n)$ with an algorithm that is known since the 70s. It essentially matches an $(m+n)^{Ω(k)}$ ETH-lower bound by Araújo, Bougeret, Campos, and Sau [Algorithmica 2023] and Dublois, Lampis, and Paschos [TCS 2022]. Many hypergraphs seen in practice have much more edges than vertices, $m \gg n$. This raises the question whether an improvement of the run time dependency on $m$ can be traded for an increase in the dependency on $n$. Our first result is an algorithm to recognize hypergraphs with transversal rank at least $k$ in time $O(Δ^{k-2} mn^{k-1})$, where $Δ\le m$ is the maximum degree. Our main technical contribution is a ``look-ahead'' method that allows us to find higher-order extensions, minimal hitting sets that augment a given set with at least two more vertices. We show that this method can also be used to enumerate all minimal hitting sets of a hypergraph with transversal rank $k^*$ with delay $O(Δ^{k^*-1} mn^2)$. We then explore the possibility of further reducing the running time for computing the transversal rank to $\textsf{poly}(m) \cdot n^{k+O(1)}$. This turns out to be equivalent to several breakthroughs in combinatorial algorithms and enumeration. Among other things, such an improvement is possible if and only if $k$-conformal hypergraphs can also be recognized in time $\textsf{poly}(m) \cdot n^{k+O(1)}$, and iff the maximal hypercliques/independent sets of a uniform hypergraph can be enumerated with incremental delay.

Quantum key distribution (QKD) is the most explored application of quantum information theory. A central problem in entanglement-based QKD (EB-QKD), is whether every entangled state can be used to extract a key. We observe that entanglement is not sufficient for standard practical EB-QKD protocols where the input choices are announced by the parties that want to share a secure key, such as E91 or entanglement-based BB84 type protocols, when even an arbitrarily small amount of leakage of classical side information occurs. We do this by identifying a class of two-qubit isotropic states that are entangled but cannot be used to distil the key under such protocols for any possible measurement by the parties. Counter-intuitively, this gap persists even when the leakage occurs from the "junk" rounds of the protocol, i.e, rounds that cannot be used to generate any key. We then extend this result to arbitrary dimensions and parties by identifying a class of isotropic states that are not useful to extract a secure key under such protocols, even if they are entangled. Finally, we demonstrate that our approach provides a tool to upper-bound the scalability of repeater-based QKD architectures in a protocol-independent manner. Interestingly, we find that allowing for even a tiny noise in the preparation drastically reduces the scalability of the QKD network.

While $β$-Ga$_2$O$_3$ is considered a promising wide bandgap semiconductor, the impact of ion-induced defect formation and anisotropic elasticity remains poorly understood. Here, we combine a simulation and experiment X-ray diffraction (XRD) study of the strain-stress dynamics induced by ion implantation into $β$-Ga$_2$O$_3$ single-crystals with different surface orientations. The strain accumulation in the out-of-plane direction is observed by XRD to occur in an anisotropic manner, with compressive strain along the [010] direction and tensile strain along the directions perpendicular to (100) and (001). An anisotropic stress/strain accumulation model is proposed and probed via Molecular Dynamics (MD), showing an excellent agreement with the experiments. For higher damage levels, pole figures obtained both experimentally and by MD via a novel reciprocal-space projection method reveal an orientation-independent $β$-to-$γ$ phase transition, with a fixed crystallographic relationship between the polymorphs. By exploring the strain-stress dynamics in anisotropic systems, this work establishes a method to directly compare macroscale diffraction experiments and atomistic simulations and opens a new path to engineer the properties of such systems utilizing their anisotropic response to ion implantation/irradiation.

We present an analytical model for intermolecular Coulombic electron capture (ICEC) which includes the internal nuclear dynamics of the molecules involved. In ICEC, an electron attaches to an atom or molecule by transferring excess energy to a neighbor, ionizing said neighbor. While previous theoretical investigations assumed fixed nuclei, recent studies indicate that relative motion between the two ICEC partners significantly influences the process. Here, we incorporate the internal nuclear motion of the molecules involved into an analytical equation of the ICEC cross section. We employ two approaches: 1. utilizing theoretical vibrationally resolved photoionization cross sections and 2. applying the Franck-Condon principle. Our theory yields electron spectra, ICEC cross sections for individual vibronic transitions, and temperature dependent cross sections. Nuclear dynamics lead to a distribution of the electronic cross section over several vibrational states and, in our model system H+ LiH, triggers dissociation of LiH during ICEC.

We introduce an $\varepsilon$-approximate unitary 2-design that is compatible with the structure of p- and q-quadratures in continuous-variable (CV) quantum systems. The design unitaries are defined on a finite-dimensional discretisation of the CV space and can be physically implemented as operations on the full CV space. This establishes the first approximate unitary design for CV systems. The design alternatingly acts with unitaries based on the quadrature operators $\hat q$ and $\hat p$. We prove that the parameter $\varepsilon$ is given by $1/d^\ell$, where $d$ is the dimension of the truncated Hilbert space and $\ell$ is the number of iterations. We propose an Unclonable Encryption scheme in which the encryption operators are given by the unitaries which constitute the approximate unitary design. We prove its security using recent results on decoupling. This establishes unclonable-indistinguishable security for a CV encryption for the first time.

We present the discovery of seven molecular clouds in the radio galaxy B2 0902+34 at redshift z=3.4. These clouds are detected as CO(0-1) absorption features against the bright radio continuum, and spectrally resolved using the Karl G. Jansky Very Large Array (VLA). The velocity dispersion of the individual absorption components ranges from 3-7 km/s, which is similar to values observed for molecular clouds in the Milky Way and nearby galaxies, and imply cloud radii of R~10$^{1-2}$ pc. The absorbing clouds are found in a region of high obscuration inside a 30 kpc wide stellar nebula, as revealed by rest-frame near-ultraviolet imaging performed with the Hubble Space Telescope (HST). The fact that we spectrally resolve molecular clouds at the onset of Cosmic Noon opens prospects for studying cloud chemistry and physics that drive the formation of stars in the Early Universe.

We present an optimization-based formulation of the Red Light Green Light (RLGL) algorithm for computing stationary distributions of large Markov chains. This perspective clarifies the algorithm's behavior, establishes exponential convergence for a class of chains, and suggests practical scheduling strategies to accelerate convergence.

Cross-chain token standards enable fungible tokens that exist across multiple blockchains with a unified total supply model. This paper presents a comprehensive comparative analysis of five leading cross-chain token standards and frameworks: the xERC20 standard (implementing ERC-7281), the Omnichain Fungible Token (OFT) standard, the Native Token Transfers (NTT) framework, the Cross-Chain Token (CCT) standard, and the SuperchainERC20 standard (implementing ERC-7802). We examine each standard's distinguishing properties and technical design, including architecture, message-passing mechanisms, interoperability scope, chain compatibility, and security features. Our analysis reveals that while all these standards share the goal of seamless cross-chain fungibility, they differ significantly in implementation approach, trust model, and target ecosystem.

We investigate the problem of compiling the generation of graph states to arbitrarily many distributed homogeneous quantum processing units (QPUs), providing a scalable partitioning algorithm and graph state generation protocol to minimize the number of Bell pairs required. To this goal, we consider the problem of balanced k graph partitioning with the objective of minimizing the sizes of the maximum matchings between partitions, a more natural measure of entanglement compared to the naive but common metric of cut edges. We show that our heuristic algorithm, BURY, partitions graph states to require fewer Bell pairs for generation than state-of-the-art k partition algorithms. Furthermore, we show that BURY reduces the cut-rank of the partitions, demonstrating that the partitioning found by our algorithm is likely to minimize the Bell pair utilization of any future improved distributed graph state generation protocol. Additionally, we discuss how one could straightforwardly apply our methods to the dynamic case where the graph state generation and measurement are performed concurrently. Our study of the balanced minimum maximum matching k partition problem and the heuristic algorithm we design provides a scalable foundation for reducing quantum network overhead for distributed measurement-based quantum computation (MBQC), as well as any scheme where distributed graph state generation is desired.

Hyperdoping, overcoming the solubility limit of dopants in a crystalline semiconductor, is a fertile method for the enhancement of the electrical, structural and optical devices' performances and for the exploration of exotic phases such as superconductivity. We demonstrate an unprecedented control on the dopant concentration and lattice deformation via nanosecond laser doping in epitaxial boron doped silicon, achieving record carrier concentrations (8 at.%) and lattice deformations (3 %). Probing the microscopical hyperdoping limitations, we show that the relevant mechanisms are caught by a simple combinatorial model, which quantitatively explains both the experimental carrier concentration and lattice deformation evolution. First principle calculations complete and support such simple model. Indeed, at the high doping levels now attainable, the maximum carrier concentration is inherently limited by the probability of two or three substitutional dopants occupying neighboring lattice sites, forming partially inactive complexes that we detail. This description is valid in the case of perfect layers with no crystallographic defects and a fully substitutional dopant occupation, highlighting the quality of the epitaxial layers realized.

Outflows of rapidly rotating protomagnetars have been considered as attractive sites for the synthesis of nuclei heavier than iron, but the question remains whether these nuclei are able to survive against photodisintegration as they make their way out of their formation environments. In this work, we present new analytic fitting formulae for the photodisintegration cross sections applicable to heavy nuclei beyond iron. We confirm that the results from the TALYS simulations are consistent with the theory of the giant dipole resonance, and apply the obtained new formulae to investigate whether ultraheavy nuclei entrained in protomagnetar outflows can be disintegrated by thermal and nonthermal photons before leaving the stellar envelope. We explore two outflow models: a spherical wind model and a jetted outflow model. For nuclei accelerated to the bulk speed of these outflows, their survival depends on the model and engine properties. For spherical winds, nuclei may survive for the first $\sim100\,{\rm s}$ post-core collapse, but as the wind Lorentz factor increases, the photodisintegration optical depth sharply rises and nuclei may no longer survive. For the jetted outflows arising from progenitors surrounded with stellar envelopes, nuclei can only survive before the jet breakout time in cases where the central engine has low spin-down energy, that is, with a low magnetic field strength and longer spin period. In progenitors with more extended envelopes, the jet break out time is much longer, allowing for nonthermal photons to readily photodisintegrate nuclei in high spin-down energy cases. These results also have implications for the capabilities of protomagnetars to source ultra-high energy cosmic ray nuclei.

We establish an asymptotic expansion in inverse powers of time of the correlation function of isometric extensions of volume-preserving Anosov flows on Abelian covers of closed manifolds.