This paper introduces a novel Multi-Agent Cooperative Learning (MACL) framework to address cross-modal alignment collapse in vision-language models when handling out-of-distribution (OOD) concepts. Four core agents, including image, text, name, and coordination agents, collaboratively mitigate modality imbalance through structured message passing. The proposed framework enables multi-agent feature space name learning, incorporates a context exchange enhanced few-shot learning algorithm, and adopts an adaptive dynamic balancing mechanism to regulate inter-agent contributions. Experiments on the VISTA-Beyond dataset demonstrate that MACL significantly improves performance in both few-shot and zero-shot settings, achieving 1-5% precision gains across diverse visual domains.

We introduce an effective framework to model star-formation burstiness and use it to jointly fit galaxy UV luminosity functions (UVLFs), clustering, and H$α$/UV ratios, providing the first robust empirical evidence that early galaxies hosted in lower-mass halos are burstier. Using $z\sim 4-6$ observations, we find that galaxies show approximately $0.6$ dex of SFR variability if hosted in halos of $M_h = 10^{11}\, M_\odot$ (typical of $M_{\rm UV}\approx -19$ galaxies at $z = 6$). This translates into a scatter of $σ_{M_{\rm UV}}\approx 0.75$ mag in the UVLF, in line with past findings. Strikingly, we find that burstiness grows for galaxies hosted in smaller halos, reaching $\gtrsim 1$ dex for $M_h \leq 10^{9}\, M_\odot$ (corresponding to $σ_{M_{\rm UV}} \approx 1.5$ mag for faint $M_{\rm UV} \gtrsim -15$ galaxies). Extrapolating to higher redshifts, when small halos were more prevalent, the inferred mass-dependent burstiness can reproduce observed UVLFs up to $z\sim 17$ within 1$σ$, potentially alleviating the tension between pre- and post-JWST galaxy-formation models. Current observations allow us to constrain the main burst timescale to approximately $20$ Myr, consistent with expectations from supernova feedback, and suggest broad distributions of ionizing efficiencies at fixed $M_{\rm UV}$. Our results demonstrate that mass-dependent burstiness, as predicted by hydrodynamical simulations, is critical for understanding the mass assembly of early galaxies.

Using deep medium-resolution JWST rest-optical spectra of a sample of typical star-forming galaxies (Lyman break galaxies and Lyman-$α$ emitters) from the LyC22 survey at $z \sim 3$, we determined the nebular abundances of N, O, and Ne relative to H for a subsample of 25 objects with the direct method, based on auroral [OIII]4363 line detections. Our measurements increases the number of accurate N/O determinations at $z \sim 2-4$ using a homogeneous approach. We found a mean value of $\log({\rm N/O})=-1.29^{+0.25}_{-0.21} $ over a metallicity range 12+log(O/H)=7.5 to 8.44. The observed N/O ratio and scatter are indistinguishable from that observed in low-z galaxies and HII regions over the same metallicity range, showing thus no redshift evolution of N/O for typical galaxies over a significant fraction of cosmic time. We also show that typical $z \sim 3$ galaxies show a similar offset in the BPT diagram as galaxies from the low-z Lyman Continuum Survey (LzLCS), when compared to the average of SDSS galaxies, and show that this offset is not due to enhanced nitrogen abundances. Our results establish a basis for future studies of the evolution of N and O at higher redshifts.

Recently, we have proposed a new free boundary problem representing the bread baking process in a hot oven. Unknown functions in this problem are the position of the evaporation front, the temperature field and the water content. For solving this problem we observed two difficulties that the growth rate of the free boundary depends on the water content and the boundary condition for the water content contains the temperature. In this paper, by improving the regularity of solutions, we overcome these difficulties and establish existence of a solution locally in time and its uniqueness. Moreover, under some sign conditions for initial data, we derive a result on the maximal interval of existence to solutions.

In an effort to compete with the brain's efficiency at processing information, neuromorphic hardware combines artificial synapses and neurons using mixed-signal circuits and emerging memories. In ferroelectric resistive weights, the strength of the synaptic connection between two neurons is stored in the device conductance. During learning, programming pulses are applied to the synaptic weight, which reconfigures the ferroelectric domains and adjusts the conductance. One strategy to lower the energy cost during the training phase is to lower the duration of the programming pulses. However, the latter cannot be shorter than the self-loading time of the resistive weights, limited by intrinsic parasitics in the circuits. In this work, ferroelectric resistive weights are fabricated using a process compatible with CMOS Back-End-Of-Line integration, based on hafnia/zirconia nanolaminates. By laterally scaling the device area under 100 $μ$m$^2$, the self-loading time becomes sufficiently short to enable 20 ns programming, which corresponds to a maximum of 3 picoJoules per pulse. Further, in this work, the weight update rule with 20 ns pulses is experimentally measured not only for different amplitudes but also for different initial conductance states. We find that the final weight is determined by the pulse amplitude, independent of the initial weight value.

Myasnikov, Ushakov, and Won introduced power circuits in 2012 to construct a polynomial-time algorithm for the word problem in the Baumslag group, which has a non-elementary Dehn function. Power circuits are computational structures that support addition and the operation $(x,y) \mapsto x \cdot 2^y$ on integers. They also posed the question of decidability of the Diophantine problem over the structure $\langle \mathbb{N}_{>0}; +, x \cdot 2^y, \leq, 1 \rangle$, which is closely related to power circuits. In this paper, we prove that the Diophantine problem over this structure is undecidable.

Context. Among options for definition of the lunar reference time, the option taking Lunar Coordinate Time (O1) has its simplicity but cannot be realized by any clock without steering, while another option adopting the lunar geoid (selenoid) proper time (O2) has its convenience for users on the lunar surface but would bring a new scaling of spatial coordinates and mass parameter of the Moon. Aims. We propose a ''time aligned orbit'' that the readings of an ideal clock in this orbit could equal to the selenoid proper time in O2 and these readings could be converted to Lunar Coordinate Time in O1 by a known linear transformation. Methods. We show that there exist the time aligned orbit around the Moon with its semi-major axis of about 1.5 lunar radius slightly depending on its inclination. We conduct a set of numerical simulations to assess to what extent a clock on these orbits could realize O2 in a more realistic lunar environment. Results. We find that the proper time in our simulations would desynchronize from the selenoid proper time up to 190 ns after a year with a frequency offset of 6E-15, which is solely 3.75% of the frequency difference in O2 caused by the lunar surface topography. These numbers might be further reduced to 13 ns and 4E-16, if we could account for the deviation of the mean orbits in our simulations from the nominal ones. Conclusions. One might simultaneously realize O1 and O2 by deployment of a single clock in the time aligned orbit. This approach also has its scalability for other terrestrial planets beyond the Earth-Moon system.

Given an abelian category and a stability condition satisfying appropriate conditions, we define generalized $K$-theoretic invariants and prove that they satisfy wall-crossing formulas. For this, we introduce a new associative algebra structure on the $K$-homology of the stack of objects of an abelian category, which we call the $K$-Hall algebra. We first define $δ$-invariants directly coming from the stack of semistable objects and use the $K$-Hall algebra to take a formal logarithm and construct $\varepsilon$-invariants. We prove that these satisfy appropriate wall-crossing formulas using the non-abelian localization theorem. Based on work of Joyce in the cohomological setting, Liu had previously defined similar invariants assuming the existence of a framing functor; we show that when their definition of invariants makes sense it agrees with ours. Our results extend Joyce--Liu wall-crossing to non-standard hearts of $D^b(X)$, for which framing functors are not known to exist.

Context: During the last decades, significant progress has been made in both numerical simulations of turbulent dynamo and theoretical understanding of turbulence. However, there is still lack of quantitative comparison between the simulations and the theory of the dynamo. Results: We study the critical magnetic Reynolds number ($Rm_c$) and the growth rate near the threshold both in the limit of very high and in the case of moderate Reynolds numbers. We argue that in Kazantsev equation for magnetic field generation, one should use the quasi-Lagrangian correlator of velocities instead of Eulerian, as usually implied when comparing theory and simulations. The theoretical results obtained with this correlator agree well with numerical results. We also propose the explanation of the decrease of $Rm_c$ as a function of Reynolds number ($Re$) at intermediate-high $Re$. It is probably due to Reynolds-dependent intermittency of the velocity structure function: we show that the scaling exponent of this function in the inertial range affects strongly the magnetic field generation, and it is known to be an increasing function of the Reynolds number. Conclusions: Use of quasi-Lagrangian correlator in the Kazantsev theory gives good accordance with numerical simulations. An ideal way to compare them should be to find the correlator substituted to the Kazantsev equation and the generation properties in the same simulation. At least one has to use universal parameters independent of the properties of pumping scale. Reynolds-dependent intermittency can explain recently observed decrease of the critical magnetic Reynolds number at small Prandtl numbers.

We propose to call a class of deformed Feynman integrals as twisted Feynman integrals, where the integrand has an additional exponential factor linear in loop momenta. Such integrals appear in various contexts: tensor reduction of Feynman integrals, Fourier transform of Feynman integrals, and spin-resummed dynamics in post-Minkowskian gravity. First, we construct a mathematical framework that manifests the geometric interpretation of twisted Feynman integrals. Next, we generalise the standard mathematical tools for studying Feynman integrals for application to their twisted cousins, and explore their mathematical properties. In particular, it is found that (i) Symanzik polynomials are no longer homogeneous and become graded, (ii) twisted Feynman integrals fall under the class of exponential periods, and (iii) the geometry of the function space cannot be inferred from the leading singularity computed through the (generalised) Baikov parametrisation of twisted Feynman integrals.

Several non-perturbative results for hot QCD are challenging some aspects of the phase diagram and its associated degrees of freedom which were previously believed to be well understood. With increasing temperature, the chiral crossover is followed by an intermediate region with an approximate chiral spin symmetry larger than chiral symmetry, in which pseudo-scalar mesons continue to exist as hadron-like excitations, before at some higher temperature the expected chiral symmetry is recovered. By testing general formal considerations against lattice data, it can be shown that thermally modified versions of stable vacuum particles, so-called thermoparticles, form the constituents of thermal quantum field theories, with properties quite different from what is expected perturbatively. This ``viewpoint'' aims to raise broader and, in particular, phenomenological interest in these directions.

We analyze a non-isothermal Darcy-Brinkman thin-film flow with a periodically oscillating boundary and viscous dissipation acting as a heat source. Using asymptotic analysis and the periodic unfolding method, we establish the convergence of velocity, pressure, and temperature fields as the small parameter (related to the film thickness and the period of the roughness) tends to zero. The limit problems depend on the relative scaling of the roughness wavelength and consist of coupled elliptic systems combining Reynolds-type equations with Darcy-Brinkman cell problems and reduced energy equation. In the critical roughness regime, the effective model exhibits a strong coupling induced by the oscillatory geometry, which does not occur in a smooth-boundary case.

Our objective is to characterize the QUIJOTE Thirty and Forty GHz instrument (TFGI), calibrate it with a reference calibration signal on the ground, compare our results with on-sky calibration based on bright sources, and study the stability of the calibration parameters over time. First, from the ground, we fit the data using a reference calibration signal (a diode) introduced to resolve degeneracies among the various instrument angles. Finally, we utilize on-sky observations of Tau A and the Moon to validate the results. By creating calibration datasets obtained with the reference diode, we evaluate the data quality and quantify phase switch errors to account for the fine polarization response. We also utilize Tau A and Moon observations to calibrate the system's response and stability over time. In addition, we calculate the refraction index of the Moon to be $n_{Moon}$ = 1.209 $\pm$ 0.007 (stat) $\pm$ 0.005 (sys) at 31 GHz under smooth-surface assumption. The results from fitting the instrument phase-switch error angle align with 0 deg at 2$σ$ precision, indicating that no further correction is required within a few percent precision. The calibrations with astrophysical sources (Tau A and the Moon) yield consistent results that constrain the polarization angle and responsivity. The polarization efficiency aligns well with ground measurements and the Tau A characterization, whereas the Moon-based calibration is more affected by systematics. We find hints of responsivity variations over time, although the relative responsivity between channels is found to remain stable. In the future, we conclude that installing a live calibrator will enhance performance by continuously monitoring responsivity and, in turn, improving the mitigation of systematic effects.

We present a quadratic estimator that detects and reconstructs spatially-varying multiplicative ($m-$) bias in weak lensing shear measurements, by exploiting the $EB$ mode coupling that it generates. The method combines $E$ and $B$ modes with inverse-variance weights, to yield an unbiased reconstruction of $m(\boldsymbolθ)$ to first order. We study the ability of future Stage IV surveys to obtain an unbiased reconstruction of the $m$-bias in differing scenarios, considering differing bias morphologies, and characteristic scales, as well as differing metrics to quantify the signal-to-noise ratio of the reconstructed map. Considering an $m$ pattern repeating on $\sim 1^\circ\times1^\circ$ sky patches, as might be the case for an $m$ field caused by focal-plane systematics. With a Euclid-like redshift distribution, we find that $\sim5\%$ rms variations in $m$-bias may be detected at the 20$σ$ level, after stacking between $\sim400$ and $\sim1000$ patches (rising to between $\sim2800$ and $\sim7600$ for $1\%$ rms variations, data volumes that are becoming available with upcoming surveys), depending on the morphology of the $m$ pattern. We show that these results are robust against the cosmological model assumed in the reconstruction, as well as the presence of intrinsic alignments or baryonic effects, and that the method shows no spurious response to additive ($c-$) bias. These results demonstrate that percent-level, spatially-varying $m-$bias can be detected at high significance, enabling diagnosis and mitigation in the Stage IV weak lensing era.

Modeling binary neutron star merger (BNSM) ejecta evolution requires simulations involving hydrodynamics, nuclear reactions, and radiative processes. The impact of nuclear burning and atomic opacity is poorly understood and often treated with simplified prescriptions. We systematically investigate different treatments of nuclear heating, thermalization, and opacities in radiation-hydrodynamics simulations of BNSM ejecta and kilonova light curves. Ejecta from long-term numerical-relativity simulations are evolved to ~30 days using a 2D ray-by-ray approach. We compare simplified heating-rates, thermalization prescriptions, and gray opacities with in-situ nuclear networks (NN) that track energy deposition, and include a composition-dependent thermalization scheme and frequency-dependent, atomic-physics-based opacities. Coupling NN and hydrodynamics affects nucleosynthesis and kilonova emission. Assuming homologous expansion alters the abundance evolution and produces a narrower second $r$-process peak and a third peak shifted to higher mass numbers. Nuclear heating back-reaction delays and reddens the early emission. A constant thermalization underestimates the early luminosity and overestimates the late emission. Analytical opacities yield dimmer and redder kilonovae at early times ($t\lesssim$ hour) and a prolonged emission at $t\gtrsim5$ days. Resolving the first hundreds of milliseconds of hydrodynamics is essential for robust nucleosynthesis calculations, and composition-dependent thermalization and frequency-dependent, atomic opacities are needed to accurately capture the ejecta temperature and kilonova brightness and color evolution. Analytic nuclear-power fits with simplified thermalization and opacities can reproduce the density and temperature evolution of the ejecta. [Abridged].

In this paper, we present a first quantitative test of detected light signals produced in a pulsed neutron source run in a small vertical drift LArTPC at the CERN neutrino platform ColdBox test facility. The ColdBox cryostat, detectors, neutron sources, and particle interactions are modeled and simulated using Fluka. A good agreement is found in the detected number of photoelectrons, with values below 650 photoelectrons in both data and simulation, for all four X-ARAPUCA photodetectors on the cathode in the LArTPC. A time constant is also fitted from the neutron-beam-off light signal spectrum and found consistent between data and MC. Several important systematic effects are discussed and serve as guides for future runs at larger LArTPCs.

We present an all-sky map of the synchrotron spectral index and curvature between 45 and 2300 MHz at a resolution of 1 degree calculated from a combination of numerous partial sky empirical measurements. We employ a least-squares parametric fit which relies on removing a free-free emission template and a component separation technique which fits for both synchrotron and free-free emission. We compare our diffuse sky model estimates against those derived from the models widely used in the community (e.g. pysm3 and GSM) employing external datasets that were not included in the estimation process. Our evaluation focuses on identifying the enhanced consistency at both the map level and in pixel-to-pixel correlations, allowing for a more robust verification of our model's performance. We find our parametric, least-squares synchrotron estimate to be the most reliable across radio frequencies as it consistently provides sky models with average accuracies (when compared to empirical data) of around 20 per cent, whilst other model performances range on average between 10 and 70 per cent accurate. The results obtained have been made publicly accessible online and can be utilized to further develop and refine models of Galactic synchrotron emission.

Based on entropy and symmetrical uncertainty (SU), we define a metric for categorical random variables and show that this metric can be promoted into an appropriate quotient space of categorical random variables. Moreover, we also show that there is a natural commutative monoid structure in the same quotient space, which is compatible with the topology induced by the metric, in the sense that the monoid operation is continuous.

Understanding intermittency of turbulent systems from the underlying differential equations is an outstanding problem in fluid dynamics. Here, in the example of Burgers turbulence as a stringent test, we introduce a method that yields high-order structure function exponents by combining instanton calculus, fusion rule predictions, and low-order statistical inputs from direct numerical simulations. We use instantons to evaluate high velocity gradient (VG) moments at the onset of intermittency, and then infer scaling exponents in fully developed turbulence via fusion rules. We show that the method captures the crossover at $\mathrm{Re}_λ\approx 1$ in the VG moment scaling, highlight the necessity of including fluctuations around instantons, and discuss future extensions.

In this work, we utilize a new suite of Milky Way-mass halos from the DREAMS Project, simulated with Cold Dark Matter (CDM), to quantify the influence of baryon feedback and intrinsic halo-to-halo variance on dark matter density profiles. Our suite of 1024 halos varies over supernova and black hole feedback parameters from the IllustrisTNG model, as well as variations in two cosmological parameters. We find that, for the DREAMS parameter variations, Milky Way-mass dark matter density profiles in the IllustrisTNG model are largely insensitive to astrophysics and cosmology variations, with the dominant source of scatter instead arising from halo-to-halo variance. However, most of the (comparatively minor) feedback-driven variations come from the changes to supernova prescriptions. By comparing to dark matter-only simulations, we find that the strongest supernova wind energies are so effective at preventing galaxy formation that the halos are nearly entirely collisionless dark matter. Finally, regardless of physics variation, all the DREAMS halos are roughly consistent with a halo contracting adiabatically from the presence of baryons, unlike models that have bursty stellar feedback. This work represents a step toward assessing the uncertainty in Milky Way dark matter profiles, with direct implications for dark matter searches where systematic uncertainty in the density profile remains a major challenge.

In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the group. We also show that the set of centralizers that are minimal under the partial ordering form a cover of the group. We show for $F$-groups that are nonabelian $p$-groups that the number of distinct nontrivial centralizers is congruent to $1$ modulo $p$.

We provide a new measurement of the expansion history of the Universe at $z=0.54$ with the cosmic chronometers (CC) method, exploiting the high-quality spectroscopic VLT/MUSE data for three galaxy clusters in close-by redshift bins: SDSS J2222+2745 ($z=0.49$), MACS J1149.5+2223 ($z=0.54$), and SDSS J1029+2623 ($z=0.59$). The central one, MACS J1149.5+2223, hosts the well-known supernova 'Refsdal', which allowed for $H_0$ measurements via time delay cosmography (TDC). This represents the first step for a self-consistent probe combination, where different methods are applied to the same data sample. After selecting the most passive and massive cluster members (38 CCs), we derive their age and physical parameters via full spectrum fitting. We use the code Bagpipes, specifically modified to remove the cosmological prior on ages. On average, the CC sample shows super-solar metallicities $Z/Z_{\odot} = 1.3 \pm 0.7$, low dust extinction $A_{\rm{V}} = 0.3 \pm 0.3$ mag and to have formed in short bursts $τ= 0.6 \pm 0.2$ Gyr. We also observe both an ageing trend in redshift and a mass-downsizing pattern. From the age-redshift trend, implementing the CC method through a bootstrap approach, we derive a new $H(z)$ measurement: $H$($z$=0.542) = $66_{-29}^{+81}$ (stat) $\pm$13 (syst) km/s/Mpc. We also simulate the impact of increased statistics and extended redshift coverage, finding that $H$($z$) uncertainties can be reduced by up to a factor of 4 with $\sim$100 CCs and a slightly broader redshift range (d$z\sim$0.2).

We study a question of Matui and varations of it on minimal ample groupoids that are neither almost finite nor purely infinite. We first observe that there are already effective minimal ample transformation groupoids that are neither almost finite nor purely infinite. These groupoids can even be chosen to be amenable. Then we construct essentially principle ample groupoids that are neither almost finite nor purely infinite. These are based on the recent twisted topological groupoid construction of Palmer and Wu. In particular our new examples do not arise from transformation groupoids.

In the space-based gravitational wave detections, the axion-like dark matter would alter the polarization state of the laser link between spacecrafts due to the birefringence effect. However, current designs of space-based laser interferometer are insensitive to variations in the polarization angle. Thus, the additional wave plates are employed to enable the response of the axion-induced birefringence effect. We calculate and compare the sensitivities of different space-based detectors, accounting for three time-delay interferometry combinations, including Monitor, Beacon, and Relay. We find that the Monitor and Beacon combinations have better sensitivity in the high-frequency range, and the optimal sensitivity reaches $g_{aγ}\sim 10^{-13}\text{GeV}^{-1}$, while the Sagnac combination is superior in the low-frequency range. We also find that ASTROD-GW can cover the detection range of axion-like dark matter mass down to $10^{-20}\text{eV}$.

We study the low-lying zeros of certain Artin $L$-functions associated with $D_4$-quartic function fields. Specifically, we prove that when ordered by conductor, at least $77\%$ of these $L$-functions are non-vanishing at the central point. This generalises and extends results over $\mathbb{Q}$ due to Durlanik, proving that an infinite number of these $L$-functions are non-vanishing. We obtain these results by examining the low-lying zeros of the $L$-functions using the one-level density. Specifically, we apply and extend a method used by Rudnick, who studied Dirichlet $L$-functions associated with quadratic function field extensions, to the $D_4$-case. The main difficulty is studying $L$-functions which are associated to $D_4$-fields whose quadratic subfield is of large discriminant. These $L$-functions are studied by utilising the so-called flipped field of a $D_4$ extension, combining a method introduced by Friedrichsen for counting $D_4$-fields, with explicit ramification theory in such fields provided by Altuğ, Shankar, Varma and Wilson.

Diffuse contamination from Galactic foreground emission is one of the main concerns for reconstruction of the cosmic microwave background (CMB) lensing potential for next-generation CMB polarisation experiments. Using realistic simulations, we investigated the impact of Galactic foreground residuals from multi-frequency foreground-cleaning methods on CMB lensing reconstruction and the de-lensing of B-mode maps. We also assessed how these residuals affect constraints on the tensor-to-scalar ratio for a CMB-S4--like experiment. We paid special attention to the errors coming from the small scale non-Gaussianity of the foreground residuals. We show that component separation is essential for the lensing reconstruction that reduces Galactic emission contribution to the lensing reconstruction errors by one order of magnitude. The residual foreground contribution is dominated by terms coming from Gaussian components of the residual maps. Errors coming from non-Gaussian components are around three orders of magnitude smaller than the Gaussian one, even for recent and the most complex models of the Galactic emission considered in this work. Although the bias in the reconstruction errors due to the Gaussian component of the residuals being small, it is comparable to the cosmic variance limit for the lensing power spectrum. For this reason, we corrected for this bias in the de-lensing of B-mode maps and constraining the tensor-to-scalar ratio. We also show that for the de-lensed B-mode maps with a simple quadratic estimator, that is, residuals of the Galactic emission after component separation, errors are two orders of magnitude smaller than uncertainties from leftover of the lensing signal. However, for high-sensitivity CMB experiments and more efficient de-lensing algorithms that remove up to 90% of the lensing signal, the foreground residuals will become one of the main sources of errors.

This paper focuses on the optimal control of a class of stochastic Volterra integral equations. Here the coefficients are regular and not assumed to be of convolution type. We show that, under mild regularity assumptions, these equations can be lifted in a Sobolev space, whose Hilbertian structure allows us to attack the problem through a dynamic programming approach. We are then able to use the theory of viscosity solutions on Hilbert spaces to characterise the value function of the control problem as the unique solution of a parabolic equation on Sobolev space. We provide applications and examples to illustrate the usefulness of our theory, in particular for a certain class of time inconsistent principal agent problems. As a byproduct of our analysis, we introduce a new Markovian approximation for Volterra type dynamics.

I analyze the decoherence of a $π$-junction qubit encoded by two co-located Majorana modes. Although not topologically protected, the qubit leverages distinct spatial profiles to couple to two independent environmental baths, realizing the phenomenon of quantum frustration. This mechanism is tested against the threat of quasiparticle poisoning (QP). I show that frustration is effective against Ohmic noise ($s=1$) and has some protection for $0.76<s<1$ sub-Ohmic noise. However, the experimentally prevalent $1/f$ noise ($s\to0$) falls deep within the model's localized phase, where frustration is insufficient. This causes spontaneous symmetry breaking and catastrophic decoherence. The qubit's viability depends on what the effective environment is that these local Majorana wave functions experience.

We develop a bootstrap approach to Euclidean two-point correlators, in the thermal or ground state of quantum mechanical systems. We formulate the problem of bounding the two-point correlator as a semidefinite programming problem, subject to the constraints of reflection positivity, the Heisenberg equations of motion, and the Kubo-Martin-Schwinger condition or ground-state positivity. In the dual formulation, the Heisenberg equations of motion become "inequalities of motion" on the Lagrange multipliers that enforce the constraints. This enables us to derive rigorous bounds on continuous-time two-point correlators using a finite-dimensional semidefinite or polynomial matrix program. We illustrate this method by bootstrapping the two-point correlators of the ungauged one-matrix quantum mechanics, from which we extract the spectrum and matrix elements of the low-lying adjoint states. Along the way, we provide a new derivation of the energy-entropy balance inequality and establish a connection between the high-temperature two-point correlator bootstrap and the matrix integral bootstrap.

Tensor networks (TNs) are one of the best available tools to study many-body quantum systems. TNs are particularly suitable for one-dimensional local Hamiltonians, while their performance for generic geometries is mainly limited by two aspects: the limitation in expressive power and the approximate extraction of information. Here we investigate the performance of superposition-of-product-states (SPS) ansatz, a variational framework structurally related to canonical polyadic tensor decomposition. The ansatz does not compress information as effectively as tensor networks, but it has the advantages (i) of allowing accurate extraction of information, (ii) of being structurally independent of the geometry of the system, (iii) of being readily parallelizable, and (iv) of allowing analytical shortcuts. We first study the typical properties of the SPS ansatz for spin-$1/2$ systems, including its entanglement entropy, and its trainability. We then use this ansatz for ground state search in tilted Ising models -- including one-dimensional and three-dimensional with short- and long-range interaction, and a random network -- demonstrating that SPS can attain high accuracy.