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1. Finding the Last Bits of Positional Information

   https://doi.org/10.1103/prxlife.2.013016  

   McGough, Lauren; Casademunt, Helena; Nikolić, Miloš; Aridor, Zoe; Petkova, Mariela D; Gregor, Thomas; Bialek, William (March 2024, PRX Life)

   In a developing embryo, information about the position of cells is encoded in the concentrations of morphogen molecules. In the fruit fly, the local concentrations of just a handful of proteins encoded by the gap genes are sufficient to specify position with a precision comparable to the spacing between cells along the anterior-posterior axis. This matches the precision of downstream events such as the striped patterns of expression in the pair-rule genes, but is not quite sufficient to define unique identities for individual cells. We demonstrate theoretically that this information gap can be bridged if positional errors are spatially correlated, with correlation lengths approximately $20\%$of the embryo length. We then show experimentally that these correlations are present, with the required strength, in the fluctuating positions of the pair-rule stripes, and this can be traced back to the gap genes. Taking account of these correlations, the available information matches the information needed for unique cellular specification, within error bars of approximately $2\%$. These observation support a precisionist view of information flow through the underlying genetic networks, in which accurate signals are available from the start and preserved as they are transformed into the final spatial patterns. Published by the American Physical Society2024 

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2. Nonlocal subpicosecond delay metrology using spectral quantum interference

   https://doi.org/10.1364/OPTICA.458565  

   Seshadri, Suparna; Lingaraju, Navin; Lu, Hsuan-Hao; Imany, Poolad; Leaird, Daniel_E; Weiner, Andrew_M (November 2022, Optica)

   Precise knowledge of position and timing information is critical to support elementary protocols such as entanglement swapping on quantum networks. While approaches have been devised to use quantum light for such metrology, they largely rely on time-of-flight (ToF) measurements with single-photon detectors and, therefore, are limited to picosecond-scale resolution owing to detector jitter. In this work, we demonstrate an approach to distributed sensing that leverages phase modulation to map changes in the spectral phase to coincidence probability, thereby overcoming the limits imposed by single-photon detection. By extracting information about the joint biphoton phase, we measure a generalized delay—the difference in signal–idler arrival, relative to local radio frequency (RF) phase modulation. For nonlocal ranging measurements, we achieve ( $2\mathrm{\sigma <\#comment/>}$) precision of $\pm <\#comment/>0.04\mathrm{p}\mathrm{s}$and for measurements of the relative RF phase, ( $2\mathrm{\sigma <\#comment/>}$) precision of $\pm <\#comment/>{0.7}^{\circ <\#comment/>}$. We complement this fine timing information with ToF data from single-photon time-tagging to demonstrate absolute measurement of time delay. By relying on off-the-shelf telecommunications equipment and standard quantum resources, this approach has the potential to reduce overhead in practical quantum networks. 

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3. Generalized Parking Function Polytopes

   https://doi.org/10.1007/s00026-023-00671-1  

   Hanada, Mitsuki; Lentfer, John; Vindas-Meléndez, Andrés_R (November 2023, Annals of Combinatorics)

   Abstract A classical parking function of lengthnis a list of positive integers$$(a_1, a_2, \ldots , a_n)$$ $(a_1,a_2,\dots ,a_n)$whose nondecreasing rearrangement$$b_1 \le b_2 \le \cdots \le b_n$$ $b_1\le b_2\le \cdots \le b_n$satisfies$$b_i \le i$$ $b_i\le i$. The convex hull of all parking functions of lengthnis ann-dimensional polytope in$${\mathbb {R}}^n$$ $R^n$, which we refer to as the classical parking function polytope. Its geometric properties have been explored in Amanbayeva and Wang (Enumer Combin Appl 2(2):Paper No. S2R10, 10, 2022) in response to a question posed by Stanley (Amer Math Mon 127(6):563–571, 2020). We generalize this family of polytopes by studying the geometric properties of the convex hull of$${\textbf{x}}$$ $x$-parking functions for$${\textbf{x}}=(a,b,\dots ,b)$$ $x=(a,b,\cdots ,b)$, which we refer to as$${\textbf{x}}$$ $x$-parking function polytopes. We explore connections between these$${\textbf{x}}$$ $x$-parking function polytopes, the Pitman–Stanley polytope, and the partial permutahedra of Heuer and Striker (SIAM J Discrete Math 36(4):2863–2888, 2022). In particular, we establish a closed-form expression for the volume of$${\textbf{x}}$$ $x$-parking function polytopes. This allows us to answer a conjecture of Behrend et al. (2022) and also obtain a new closed-form expression for the volume of the convex hull of classical parking functions as a corollary. 

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4. Conformal geometry from entanglement

   https://doi.org/10.21468/SciPostPhys.18.3.102  

   Kim, Isaac H; Li, Xiang; Lin, Ting-Chun; McGreevy, John; Shi, Bowen (January 2025, SciPost Physics)

   In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap. We introduce a novel pair of information-theoretic quantities(\mathfrak{c}_{\textrm{tot}}, \eta) $({𝔠}_{\text{tot}},\eta )$that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure. We posit that, for a topological groundstate, the quantity\mathfrak{c}_{\textrm{tot}} ${𝔠}_{\text{tot}}$is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i)\mathfrak{c}_{\textrm{tot}} ${𝔠}_{\text{tot}}$is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii)\eta $\eta$is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on groundstate entanglement. We show that stationarity of\mathfrak{c}_{\textrm{tot}} ${𝔠}_{\text{tot}}$is equivalent to a vector fixed-point equation involving\eta $\eta$, making our assumption locally checkable. We also derive similar results for 1+1D systems under a suitable set of assumptions. 

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5. Kinetic-scale Current Sheets in the Solar Wind at 1 au: Scale-dependent Properties and Critical Current Density

   https://doi.org/10.3847/2041-8213/ac4fc4  

   Vasko, I. Y.; Alimov, K.; Phan, T.; Bale, S. D.; Mozer, F. S.; Artemyev, A. V. (February 2022, The Astrophysical Journal Letters)

   Abstract We present analysis of 17,043 proton kinetic-scale current sheets (CSs) collected over 124 days of Wind spacecraft measurements in the solar wind at 11 samples s⁻¹magnetic field resolution. The CSs have thickness,λ,from a few tens to one thousand kilometers with typical values around 100 km, or within about 0.1–10λ_pin terms of local proton inertial length,λ_p. We found that the current density is larger for smaller-scale CSs,J₀≈ 6 nAm⁻²· (λ/100 km)^−0.56, but does not statistically exceed a critical value,J_A,corresponding to the drift between ions and electrons of local Alvén speed. The observed trend holds in normalized units: $J_0/J_A\approx 0.17·{\left(\lambda /{\lambda }_p\right)}^{-0.51}$. The CSs are statistically force-free with magnetic shear angle correlated with CS spatial scale: $\mathrm{\Delta }\theta \approx 19°·{\left(\lambda /{\lambda }_p\right)}^{0.5}$. The observed correlations are consistent with local turbulence being the source of proton kinetic-scale CSs in the solar wind, while the mechanisms limiting the current density remain to be understood. 

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