The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors of the non-Hermitian operators that generate the dynamics, i.e., quantum channels (Markov chains). However, since these operators are non-Hermitian, their spectra are an unreliable guide to dynamical relaxation timescales or to stability against perturbations. We propose an alternative dynamical criterion for a steady state to be in a stable phase, which we name uniformity: Informally, our criterion amounts to requiring that, under sufficiently small local perturbations of the dynamics, the unperturbed and perturbed steady states are related to one another by a finite-time dissipative evolution. We show that this criterion implies many of the properties one would want from any reasonable definition of a phase. We prove that uniformity is satisfied in a canonical classical cellular automaton, and we provide numerical evidence that the gap determines the relaxation rate between nearby steady states in the same phase, a situation we conjecture holds generically whenever uniformity is satisfied. We further conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability. Published by the American Physical Society 2024

Let f \in S_{k}(\Gamma_{1}(N)) be a primitive holomorphic form of arbitrary weight k and level N . We show that the completed L -function of f has \Omega(T^{\delta}) simple zeros with imaginary part in [-T, T] , for any \delta <{2/27} . This is the first power bound in this problem for f of non-trivial level, where previously the best results were \Omega(\log\log\log{T}) for N odd, due to Booker, Milinovich, and Ng, and infinitely many simple zeros for N even, due to Booker. In addition, for f of trivial level ( N=1 ), we also improve an old result of Conrey and Ghosh on the number of simple zeros.

Epithelial cells generate functional tissues in developing embryos through collective movements and shape changes. In some morphogenetic events, a tissue dramatically reorganizes its internal structure—often generating high degrees of structural disorder—to accomplish changes in tissue shape. However, the origins of structural disorder in epithelia and what roles it might play in morphogenesis are poorly understood. We study this question in the germband epithelium, which undergoes dramatic changes in internal structure as cell rearrangements drive elongation of the embryo body axis. Using two order parameters that quantify volumetric and shear disorder, we show that structural disorder increases during body axis elongation and is strongly linked with specific developmental processes. Both disorder metrics begin to increase around the onset of axis elongation, but then plateau at values that are maintained throughout the process. Notably, the disorder plateau values for volumetric disorder are similar to those for random cell packings, suggesting this may reflect a limit on tissue behavior. In mutant embryos with disrupted external stresses from the ventral furrow, both disorder metrics reach wild-type maximum disorder values with a delay, correlating with delays in cell rearrangements. In contrast, in mutants with disrupted internal stresses and cell rearrangements, volumetric disorder is reduced compared to wild type, and shear disorder depends on specific external stress patterns. Together, these findings demonstrate that internal and external stresses both contribute to epithelial tissue disorder and suggest that the maximum values of disorder in a developing tissue reflect physical or biological limits on morphogenesis. Published by the American Physical Society 2024

We describe a general procedure for mapping arbitrary n-qubit states to two-dimensional (2D) vector fields. The mappings use complex rational function representations of individual qubits, producing classical vector field configurations that can be interpreted in terms of 2D inviscid fluid flows or electric fields. Elementary qubits are identified with localized defects in 2D harmonic vector fields, and multiqubit states find natural field representations via complex superpositions of vector field products. In particular, separable states appear as highly symmetric flow configurations, making them both dynamically and visually distinct from entangled states. The resulting real-space representations of entangled qubit states enable an intuitive visualization of their transformations under quantum logic operations. We demonstrate this for the quantum Fourier transform and the period finding process underlying Shor's algorithm, along with other quantum algorithms. Due to its generic construction, the mapping procedure suggests the possibility of extending concepts such as entanglement or entanglement entropy to classical continuum systems, and thus may help guide new experimental approaches to information storage and nonstandard computation. Published by the American Physical Society 2024

We place limits on dark matter made up of compact objects significantly heavier than a solar mass, such as MACHOs or primordial black holes (PBHs). In galaxies, the gas of such objects is generally hotter than the gas of stars and will thus heat the gas of stars even through purely gravitational interactions. Ultrafaint dwarf galaxies (UFDs) maximize this effect. Observations of the half-light radius in UFDs thus place limits on MACHO dark matter. We build upon previous constraints with an improved heating rate calculation including both direct and tidal heating, and consideration of the heavier mass range above 104M⊙. Additionally we find that MACHOs may lose energy and migrate in to the center of the UFD, increasing the heat transfer to the stars. UFDs can constrain MACHO dark matter with masses between about 10M⊙ and 108M⊙ and these are the strongest constraints over most of this range. Published by the American Physical Society 2024

Temozolomide (TMZ) treatment has demonstrated, but variable, impact on glioma prognosis. This study examines associations of survival with DNA repair gene germline polymorphisms among glioma patients who did and did not have TMZ treatment. Identifying genetic markers which sensitize tumor cells to TMZ could personalize therapy and improve outcomes. We evaluated TMZ-related survival associations of pathogenic germline SNPs and genetically predicted transcript levels within 34 DNA repair genes among 1504 glioma patients from the UCSF Adult Glioma Study and Mayo Clinic whose diagnoses spanned pre- and post-TMZ eras within the major known glioma prognostic molecular subtypes. Among those who received TMZ, 5 SNPs were associated with overall survival, but not in those who did not receive TMZ. Only rs2308321-G, in MGMT , was associated with decreased survival (HR=1.21, p=0.019) for all glioma subtypes. Rs73191162-T (near UNG ), rs13076508-C (near PARP3 ), rs7840433-A (near NEIL2 ), and rs3130618-A (near MSH5 ) were only associated with survival and TMZ treatment for certain subtypes, suggesting subtype-specific germline chemo-sensitization. Genetically predicted elevated compared to normal brain expression of PNKP was associated with dramatically worse survival for TMZ-treated patients with IDH -mutant and 1p/19q non-codeleted gliomas (p=0.015). Similarly, NEIL2 and TDG expressions were associated with altered TMZ-related survival only among certain subtypes. Functional germline alterations within DNA repair genes were associated with TMZ sensitivity, measured by overall survival, among adults with glioma, these variants should be evaluated in prospective analyses and functional studies. We observed SNPs associated with glioma survival, specific to cases receiving TMZ An MGMT variant may reduce glioma survival indirectly through myelosuppression Decreased genetic PNKP expression in the brain may sensitize cells to TMZ. The introduction of temozolomide (TMZ) as a part of standard-of-care in the treatment of gliomas marked the last notable increase in patient survival. However, the effectiveness of TMZ is not universal, and can result in serious complications. The mechanism of action behind the drug is the introduction of damaging methyl groups across the tumor genome and leveraging of DNA damage repair (DDR) mechanisms to signal programmed cell death. Previous literature has identified that defects in DDR mechanisms can alter TMZ sensitivity. Using a unique dataset that spans the pre- and post-TMZ eras, we demonstrate that germline variation in DDR-related genes may have significant impact on overall survival for patients treated with TMZ, with no effects observed in the pre-TMZ era. This suggests that germline variants in these DDR genes could be used to personalize TMZ therapy to improve patient survival.

Motivated by the pair-density-wave (PDW) state found in the one-dimensional Kondo-Heisenberg chain, we report on a determinant quantum MonteCarlo study of pair fields for a two-dimensional half-filled Hubbard layer coupled to an itinerant, noninteracting layer with one electron per site. In a specific range of interlayer hopping, the pairing vertex associated with PDW order becomes more attractive than that for uniform d-wave pairing, although both remain subdominant to the leading antiferromagnetic correlations at half filling. Our result sheds light on where one potentially may find a PDW state in such a model.