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At least 91 records · Page 5

A new perspective on the integrability of Inozemtsev’s elliptic spin chain

The aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing the chaotic vs. integrable behavior of a quantum system, formulated in terms of statistical properties of its spectrum. More precisely, we study the distribution of consecutive levels of the (unfolded) spectrum, the power spectrum of the spectral fluctuations, the average degeneracy, and the equivalence to a classical vertex model. Our results are consistent with the general consensus that this model is integrable, and that it is closer in this respect to the Heisenberg chain than to its trigonometric limit (the Haldane–Shastry chain). On the other hand, we present some numerical and analytical evidence showing that the level density of Inozemtsev’s chain is asymptotically Gaussian as the number of spins tends to infinity, as is the case with the Haldane–Shastry chain. We are also able to compute analytically the mean and the standard deviation of the spectrum, showing that their asymptotic behavior coincides with that of the Haldane–Shastry chain. - Highlights: • Construction of Inozemtsev’s elliptic spin chain using Polychronakos’s freezing trick. • Numerical evidence of the Gaussian character of the level density. • Exact computation and asymptotics of the mean and standard deviation of the spectrum. • Evidence of the chain’s integrability from key statistical properties of its spectrum. • Exact evaluation of finite sums of powers of Weierstrass’s elliptic function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exact quantisation of the relativistic Hopfield model

We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields, represented by a mesoscopic polarisation field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalised Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Reinforcement Learning for feedback-enabled cyber resilience

The rapid growth in the number of devices and their connectivity has enlarged the attack surface and made cyber systems more vulnerable. As attackers become increasingly sophisticated and resourceful, mere reliance on traditional cyber protection, such as intrusion detection, firewalls, and encryption, is insufficient to secure the cyber systems. Cyber resilience provides a new security paradigm that complements inadequate protection with resilience mechanisms. A Cyber-Resilient Mechanism (CRM) adapts to the known or zero-day threats and uncertainties in real-time and strategically responds to them to maintain the critical functions of the cyber systems in the event of successful attacks. Feedback architectures play a pivotal role in enabling the online sensing, reasoning, and actuation process of the CRM. Reinforcement Learning (RL) is an important gathering of algorithms that epitomize the feedback architectures for cyber resilience. It allows the CRM to provide dynamic and sequential responses to attacks with limited or without prior knowledge of the environment and the attacker. In this work, we review the literature on RL for cyber resilience and discuss the cyber-resilient defenses against three major types of vulnerabilities, i.e., posture-related, information-related, and human-related vulnerabilities. Here we introduce moving target defense, defensive cyber deception, and assistive human security technologies as three application domains of CRMs to elaborate on their designs. The RL algorithms also have vulnerabilities themselves. We explain the major vulnerabilities of RL and present develop several attack models where the attacker target the information exchanged between the environment and the agent: the rewards, the state observations, and the action commands. We show that the attacker can trick the RL agent into learning a nefarious policy with minimum attacking effort. The paper introduces several defense methods to secure the RL-enabled systems from these attacks. However, there is still a lack of works that focuses on the defensive mechanisms for RL-enabled systems. Last but not least, we discuss the future challenges of RL for cyber security and resilience and emerging applications of RL-based CRMs.

97 MATHEMATICS AND COMPUTING↗

Logistic Regression in Clinical Studies

• A logistic regression model is used when the outcome of interest is binary. The term “logistic” refers to the underlying “logit” (log odds) function that is used to model the binary outcome. • Odds ratios are produced from a logistic regression model and have a useful interpretation. • Tips, tricks and concepts used to fit logistic regression models are similar to those used in linear regression models. • Modeling building that is knowledge-based rather than automatic is preferred in most applications of logistic regression. • A logistic regression model that is overparameterized (ie, too many variables for too few events) can result in odds ratios that are implausibly large and confidence intervals that are wide and uninterpretable. These types of “overfitted” models should be avoided. • Logistic regression models can be fit using most standard statistical software.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

3D treatment planning systems

Three-dimensional (3D) treatment planning systems have evolved and become crucial components of modern radiation therapy. The systems are computer-aided designing or planning softwares that speed up the treatment planning processes to arrive at the best dose plans for the patients undergoing radiation therapy. Furthermore, the systems provide new technology to solve problems that would not have been considered without the use of computers such as conformal radiation therapy (CRT), intensity-modulated radiation therapy (IMRT), and volumetric modulated arc therapy (VMAT). The 3D treatment planning systems vary amongst the vendors and also the dose delivery systems they are designed to support. As such these systems have different planning tools to generate the treatment plans and convert the treatment plans into executable instructions that can be implemented by the dose delivery systems. The rapid advancements in computer technology and accelerators have facilitated constant upgrades and the introduction of different and unique dose delivery systems than the traditional C-arm type medical linear accelerators. The focus of this special issue is to gather relevant 3D treatment planning systems for the radiation oncology community to keep abreast of technology advancement by assess the planning tools available as well as those unique ''tricks or tips'' used to support the different dose delivery systems.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Best Practices for the Synthesis, Activation, and Characterization of Metal–Organic Frameworks

Metal–organic frameworks (MOFs) are structurally diverse materials comprised of inorganic and organic components. As the rapidly expanding field of MOF research has demonstrated, these materials are being explored for a wide variety of potential applications. In this tutorial review, we give an overview of the current best practices associated with the synthesis, activation, and characterization of MOFs. Methods described include supercritical CO 2 activation, single crystal X-ray diffraction (XRD), powder X-ray diffraction (PXRD), nitrogen adsorption/desorption isotherms, surface area calculations, aqueous stability tests, scanning electron microscopy (SEM), inductively coupled plasma optical emission spectroscopy (ICP-OES), nuclear magnetic resonance spectroscopy (NMR), and diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). A variety of different MOFs are presented to aid in the discussion of relevant techniques. In addition, some sections are accompanied by instructional videos to give further insight into the techniques, including tips, tricks, and suggestions only those at the bench could describe.

36 MATERIALS SCIENCE↗

Twisting the Hubbard model into the momentum-mixing Hatsugai–Kohmoto model

The Hubbard model is a standard theoretical tool for studying materials with strong electron–electron interactions, such as cuprate superconductors. Unfortunately, interaction-driven phenomena, such as a transition into the strongly correlated Mott insulator phase, are difficult to treat with established theoretical techniques. However, the exactly solvable Hatsugai–Kohmoto model displays similar Mott physics. In this work we show how the Hatsugai–Kohmoto model can be deformed continuously into the Hubbard model. The trick is to systematically reintroduce all the momentum mixing that the original Hatsugai–Kohmoto model omits. This can be accomplished by grouping n momenta into a cell and hybridizing them, resulting in the momentum-mixing Hatsugai–Kohmoto model. We recover the Bethe ansatz ground-state energy of the one-dimensional Hubbard model to within 1% from only ten mixed momenta. Overall, the convergence scales as 1/n2 as opposed to the inverse linear behaviour of standard finite-cluster techniques. Our results for a square lattice reproduce all the known features from state-of-the-art simulations also with only a few mixed momenta. Consequently, we believe that the momentum-mixing Hatsugai–Kohmoto model offers an alternative tool for strongly correlated quantum matter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Site specific N- and O-glycosylation mapping of the spike proteins of SARS-CoV-2 variants of concern

Abstract The glycosylation on the spike (S) protein of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes COVID-19, modulates the viral infection by altering conformational dynamics, receptor interaction and host immune responses. Several variants of concern (VOCs) of SARS-CoV-2 have evolved during the pandemic, and crucial mutations on the S protein of the virus have led to increased transmissibility and immune escape. In this study, we compare the site-specific glycosylation and overall glycomic profiles of the wild type Wuhan-Hu-1 strain (WT) S protein and five VOCs of SARS-CoV-2: Alpha, Beta, Gamma, Delta and Omicron. Interestingly, both N- and O-glycosylation sites on the S protein are highly conserved among the spike mutant variants, particularly at the sites on the receptor-binding domain (RBD). The conservation of glycosylation sites is noteworthy, as over 2 million SARS-CoV-2 S protein sequences have been reported with various amino acid mutations. Our detailed profiling of the glycosylation at each of the individual sites of the S protein across the variants revealed intriguing possible association of glycosylation pattern on the variants and their previously reported infectivity. While the sites are conserved, we observed changes in the N- and O-glycosylation profile across the variants. The newly emerged variants, which showed higher resistance to neutralizing antibodies and vaccines, displayed a decrease in the overall abundance of complex-type glycans with both fucosylation and sialylation and an increase in the oligomannose-type glycans across the sites. Among the variants, the glycosylation sites with significant changes in glycan profile were observed at both the N -terminal domain and RBD of S protein, with Omicron showing the highest deviation. The increase in oligomannose-type happens sequentially from Alpha through Delta. Interestingly, Omicron does not contain more oligomannose-type glycans compared to Delta but does contain more compared to the WT and other VOCs. O-glycosylation at the RBD showed lower occupancy in the VOCs in comparison to the WT. Our study on the sites and pattern of glycosylation on the SARS-CoV-2 S proteins across the VOCs may help to understand how the virus evolved to trick the host immune system. Our study also highlights how the SARS-CoV-2 virus has conserved both N - and O - glycosylation sites on the S protein of the most successful variants even after undergoing extensive mutations, suggesting a correlation between infectivity/ transmissibility and glycosylation.

60 APPLIED LIFE SCIENCES↗

Using the Chebychev expansion in quantum transport calculations

Irradiation by laser pulses and a fluctuating surrounding liquid environment can, for example, lead to time-dependent effects in the transport through molecular junctions. From the theoretical point of view, time-dependent theories of quantum transport are still challenging. In one of these existing transport theories, the energy-dependent coupling between molecule and leads is decomposed into Lorentzian functions. This trick has successfully been combined with quantum master approaches, hierarchical formalisms, and non-equilibrium Green’s functions. The drawback of this approach is, however, its serious limitation to certain forms of the molecule-lead coupling and to higher temperatures. Tian and Chen [J. Chem. Phys. 137, 204114 (2012)] recently employed a Chebychev expansion to circumvent some of these latter problems. Here, we report on a similar approach also based on the Chebychev expansion but leading to a different set of coupled differential equations using the fact that a derivative of a zeroth-order Bessel function can again be given in terms of Bessel functions. Test calculations show the excellent numerical accuracy and stability of the presented formalism. The time span for which this Chebychev expansion scheme is valid without any restrictions on the form of the spectral density or temperature can be determined a priori.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DyFe 2 O 4 : A new trigonal rare-earth ferrite grown by molecular-beam epitaxy

Using epitaxial stabilization, we synthesized single-phase (001)-oriented thin films of DyFe 2 O 4+x on (111) MgAl 2 O 4 substrates by molecular-beam epitaxy. The metastable DyFe 2 O 4 polymorph formed is isostructural to known trigonal ferrimagnetic RFe 2 O 4 phases with space group $R\bar{3}m$, where R = Ho to Lu. The epitaxial DyFe 2 O 4 thin films have two in-plane orientation relationships: [100] DyFe 2 O 4 || [$2\bar{1}1$] MgAl 2 O 4 plus a twin variant related by a 60° in-plane rotation. DyFe 2 O 4 is not bulk stable and has never been synthesized before. Indeed, it has been predicted to be on the edge energetically of what may be possible to stabilize. The fact that the RFe 2 O 4 phase is stable for all elements leading up to dysprosium (Ho–Lu) leads us to believe that DyFe 2 O 4 could be a “remnant metastable phase,” one which, given the right thermodynamic conditions, could become the lowest free energy phase. We find that although we are able to get structurally very close to $R\bar{3}m$ DyFe 2 O 4 , the films are not stoichiometric as they have an increased c lattice parameter, indicative of extra oxygen as is sometimes seen in other RFe2O4 phases. The unintended surplus oxygen opens questions regarding what may be achievable using such tricks as epitaxial stabilization to access metastable phases and whether this indeed constitutes “remnant metastability.”

36 MATERIALS SCIENCE↗

Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can also be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to the chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases, the free energy is determined by the spectral density. The chaotic four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. On the other hand, the low-temperature free energy of the two-body SYK model is not flat; in fact, it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive in the low-temperature phase, which most likely is a consequence of the non-hermiticity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Lensing simulations by Taylor expansion — not so inefficient after all

Cosmic Microwave Background lensing simulation by Taylor expansion has long been considered impractical due to slow convergence, but a recent flat-sky implementation shows that a simple trick eliminates this problem, making Taylor lensing a fast and simple lensing algorithm for the flat sky. Here we generalize the method to the full sky, and study its convergence and performance relative to a commonly used numerical code, Lenspix, with extensive benchmarks of both. Compared to the flat sky case, the method takes a speed hit due to the slow speed of spherical harmonic transforms compared to fast Fourier transforms, resulting in speeds of 1/3 to 2/3 of Lenspix for similar accuracy.

79 ASTRONOMY AND ASTROPHYSICS↗

Efficient Data-Driven Geologic Feature Characterization from Pre-stack Seismic Measurements using Randomized Machine-Learning Algorithm

Conventional seismic techniques for detecting the subsurface geologic features are challenged by limited data coverage, computational inefficiency and subjective human factors. We developed a novel data-driven geological feature characterization approach based on pre-stack seismic measurements. Our characterization method employs an efficient and accurate machine learning method to extract useful subsurface geologic features automatically. Specifically, we use kernel ridge regression to account for the nonlinear relationship between seismic data and geological features. We moreover employ kernel tricks to avoid the explicit nonlinear mapping and infinite dimension of feature space. Yet, the conventional kernel ridge regression can be computationally prohibitive because of the large volume of seismic measurements. We employ a data reduction technique in combination with the conventional kernel ridge regression method to improve the computational efficiency and reduce memory usage. In particular, we utilize a randomized numerical linear algebra technique, named Nyström method, to effectively reduce the dimensionality of the feature space without compromising the information content required for accurate characterization. We provide thorough computational cost analysis to show the efficiency of our new geological feature characterization methods. We validate the performance of our method in characterizing geologic fault zones because faults play an important role in various subsurface applications. Our numerical examples demonstrate that our new characterization method significantly improves the computational efficiency while maintaining comparable accuracy. Interestingly, we demonstrate that our approach yields a speedup ratio on the order of ~102 to ~103 in a multicore computational environment.

58 GEOSCIENCES↗

Black Hole Airy Tail

In Jackiw-Teitelboim (JT) gravity, which is dual to a random matrix ensemble, the annealed entropy differs from the quenched entropy at low temperatures and goes negative. However, computing the quenched entropy in JT gravity requires a replica limit that is poorly understood. To circumvent this, we define an intermediate quantity called the semiquenched entropy, which has the positivity properties of the quenched entropy, while requiring a much simpler replica trick. We compute this in JT gravity in different regimes using (i) a bulk calculation involving wormholes corresponding to the Airy limit of the dual matrix integral and (ii) a boundary calculation involving one-eigenvalue instanton saddles proposed by Hernández-Cuenca, demonstrating consistency between these two calculations in their common regime of validity. We also clarify why similar one-eigenvalue instanton saddles cannot be used to compute the quenched entropy due to a breakdown of the saddle-point approximation for the one-eigenvalue instanton in the replica limit. Our results show how to use the gravitational path integral to prove that black holes in JT gravity have isolated ground states and to study their properties.

Gauge-gravity dualities↗

Scaling functions for eigenstate entanglement crossovers in harmonic lattices

For quantum matter, eigenstate entanglement entropies obey an area law or log-area law at low energies and small subsystem sizes and cross over to volume laws for high energies and large subsystems. This transition is captured by crossover functions, which assume a universal scaling form in quantum critical regimes. We demonstrate this for the harmonic lattice model, which describes quantized lattice vibrations and is a regularization for free scalar field theories, modeling, e.g., spin-0 bosonic particles. In one dimension, the ground-state entanglement obeys a log-area law. For dimensions d ≥ 2, it displays area laws, even at criticality. The distribution of excited-state entanglement entropies is found to be sharply peaked around subsystem entropies of corresponding thermodynamic ensembles in accordance with the eigenstate thermalization hypothesis. Numerically, we determine crossover scaling functions for the quantum critical regime of the model and do a large-deviation analysis. We show how infrared singularities of the system can be handled and how to access the thermodynamic limit using a perturbative trick for the covariance matrix. Eigenstates for quasi-free bosonic systems are not Gaussian. Here, we resolve this problem by considering appropriate squeezed states instead. For these, entanglement entropies can be evaluated efficiently.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Entanglement transitions from holographic random tensor networks

Here, we introduce a class of phase transitions separating quantum states with different entanglement features. An example of such an “entanglement phase transition” is provided by the many-body localization transition in disordered quantum systems, as it separates highly entangled thermal states at weak disorder from many-body localized states with low entanglement at strong disorder. In the spirit of random matrix theory, we describe a simple model for such transitions where a physical quantum many-body system lives at the “holographic” boundary of a bulk random tensor network. Using a replica trick approach, we map the calculation of the entanglement properties of the boundary system onto the free energy cost of fluctuating domain walls in a classical statistical mechanics model. This allows us to interpret transitions between volume-law and area-law scaling of entanglement as ordering transitions in this statistical mechanics model. Our approach allows us to get an analytic handle on the field theory of these entanglement transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nuclear-Level Effective Theory of 𝜇 → 𝑒 Conversion

The Mu2e and COMET 𝜇 → 𝑒 conversion experiments are expected to significantly advance limits on new sources of charged lepton flavor violation. Almost all theoretical work in the field has focused on just two operators. However, general symmetry arguments lead to a 𝜇 → 𝑒 conversion rate with six response functions, each of which, in principle, is observable by varying nuclear properties of targets. We construct a nucleon-level nonrelativistic effective theory (NRET) to clarify the microscopic origin of these response functions and to relate rate measurements in different targets. This exercise identifies three operators and their small parameters that control the NRET operator expansion. We note inconsistencies in past treatments of these parameters. The NRET is technically challenging, involving 16 operators, several distorted electron partial waves, bound muon upper and lower components, and an exclusive nuclear matrix element. We introduce a trick for treating the electron Coulomb effects accurately, which enables us to include all of these effects while producing transition densities whose one-body matrix elements can be evaluated analytically, greatly simplifying the nuclear physics. We derive bounds on operator coefficients from existing and anticipated 𝜇 → 𝑒 conversion experiments. We discuss how similar NRET formulations have impacted dark matter phenomenology, noting that the tools this community has developed could be adapted for charged lepton flavor violation studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Graph-Net with Node Embeddings to Detect False Data Injection Attacks in Photovoltaic Systems

Distributed energy resources (DER) contribute to the operational stability of the larger power grid both at utility-scale as well as commercial and residential scales in aggregated forms. These DER in-turn are susceptible to increasing cyber threats. An adversary can plug into the same local network that a field photovoltaic (PV) system uses to interconnect its data loggers and inverters and manipulate certain measurements collected from the network or trick existing irradiance and inverter readings through false data injection attacks (FDIA). Control routines that rely on these measurements can propagate the false data, impacting critical decisions that result in a suboptimal operation or even cause intentional harm leading to inverter-tripping or unscheduled loads that need to be shed. To detect FDIA in PV systems, the paper introduces an attention-based graph neural network with node embeddings and applied it to a simple prototypical DC-coupled microgrid with PV, energy storage, and load. The algorithm shows a detection accuracy of up to 98.95%. The proposed FDIA detection technique will provide micro-grid operators with an effective method to safeguard their systems, guaranteeing the secure and reliable operation.

Parvez, Imtiaz [Utah Valley University]↗