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1. Photonic Interference Beyond Two Modes

   Richard Oliver, Miri Blau (July 2023, Optica Quantum 2.0 Conference)

   We propose multipartite Bragg-scattering to perform all-to-all transformation among N frequency modes, realizing a bosonic N-level system. We demonstrate the N = 3 case illustrating a pathway towards scalability for frequency-domain optical quantum information systems. 

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2. Frequency-Domain Characterization of Finite Sample Linear Systems with Uniform Window Inputs

   https://doi.org/10.3390/signals6010001  

   Zhou, Qihou (March 2025, Signals)

   We discuss determining a finite sample linear time-invariant (FS-LTI) system’s impulse response function, h[n], in the frequency domain when the input testing function is a uniform window function with a width of L and the output is limited to a finite number of effective samples, M. Assuming that the samples beyond M are all zeros, the corresponding infinite sample LTI (IS-LTI) system is a marginally stable system. The ratio of the discrete Fourier transforms (DFT) of the output to input of such an FS-LTI system, H0[k], cannot be directly used to find h[n] via inverse DFT (IDFT). Nevertheless, H0[k] contains sufficient information to determine the system’s impulse response function (IRF). In the frequency-domain approach, we zero-pad the output array to a length of N. We present methods to recover h[n] from H0[k] for two scenarios: (1) N≥max(L,M+1) and N is a coprime of L, and (2) N≥L+M+1. The marginal stable system discussed here is an artifact due to the zero-value assumption on unavailable samples. The IRF obtained applies to any LTI system up to the number of effective data samples, M. In demonstrating the equivalence of H0[k] and h[n], we derive two interesting DFT pairs. These DFT pairs can be used to find trigonometric sums that are otherwise difficult to prove. The frequency-domain approach makes mitigating the effects of interferences and random noise easier. In an example application in radar remote sensing, we show that the frequency-domain processing method can be used to obtain finer details than the range resolution provided by the radar system’s transmitter. 

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3. A droplet digital PCR assay to measure pilin antigenic variation frequency in Neisseria gonorrhoeae

   https://doi.org/10.1128/msphere.00094-25  

   Quillin, Sarah J; Luo, Di; Gavagan, Aoife; Prindle, Arthur; Seifert, H Steven (May 2025, mSphere)

   D'Orazio, Sarah_E F (Ed.)

   ABSTRACT The strict human pathogenNeisseria gonorrhoeae(gonococcus [Gc]) infects an estimated 82 million individuals globally and is a World Health Organization-designated bacterial pathogen of public health importance due to escalating antimicrobial resistance. Gc vaccines have been hindered by Gc’s ability to evade immune surveillance in part by varying its major surface antigens like the type IV pilus. We developed a quick and precise method for measuring pilin antigenic variation (Av) frequency using droplet digital PCR (ddPCR) technology. Two fluorescent probes were designed to detect either the hypervariable tail region of silent pilin locuspilS3-copy 1 (S3C1) or a sequence conserved in allpilEvariants (CYS2). The appropriate frequency of pilin antigenic variation is measured by the proportion ofpilEamplicons carrying the recombinant S3C1 copy relative to the total pilE amplicons measured by CYS2. The ddPCR assay is specific for RecA-dependent pilin antigenic variation. The reduced frequency of pilin Av in strains lacking RecA-modulating recombination protein RecX and the DNA helicase RecQ confirms the ability of the assay to measure changes in pilin Av frequency. We used the ddPCR assay to determine that pilin Av frequency is altered by the colony densities on a solid medium. The ddPCR assay is an accurate, efficient way to measure Gc pilin Av frequency. IMPORTANCEGonorrhea is a sexually transmitted infectious disease of the human genital and nasopharyngeal mucosa caused by the host-restricted bacteriumNeisseria gonorrhoeae. The rise of antibiotic-resistant gonorrhea is an urgent global threat to public health. Pilus antigenic variation is a gene conversion process that allowsN. gonorrhoeaeto evade host immune surveillance, and a mechanistic understanding of this process is crucial to understandingN. gonorrhoeaepathogenesis. This report shows that we can adopt a digital PCR methodology to quickly and accurately measure pilin antigenic variation. 

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4. Century-scale wood nitrogen isotope trajectories from an oak savanna with variable fire frequencies

   https://doi.org/10.5194/bg-17-4509-2020  

   Trumper, Matthew L.; Griffin, Daniel; Hobbie, Sarah E.; Howard, Ian M.; Nelson, David M.; Reich, Peter B.; McLauchlan, Kendra K. (January 2020, Biogeosciences)

   Abstract. Fire frequency exerts a fundamental control on productivity and nutrientcycling in savanna ecosystems. Individual fires often increaseshort-term nitrogen (N) availability to plants, but repeated burningcauses ecosystem N losses and can ultimately decrease soil organicmatter and N availability. However, these effects remain poorlyunderstood due to limited long-term biogeochemical data. Here, weevaluate how fire frequency and changing vegetation compositioninfluenced wood stable N isotopes (δ15N) across space andtime at one of the longest running prescribed burn experimentsin the world (established in 1964). We developed multiple δ15N recordsacross a burn frequency gradient from precisely dated Quercus macrocarpa tree rings in an oak savanna at Cedar Creek EcosystemScience Reserve, Minnesota, USA. Sixteen trees were sampled across fourtreatment stands that varied with respect to the temporal onset of burning and burnfrequency but were consistent in overstory species representation, soilcharacteristics, and topography. Burn frequency ranged from an unburnedcontrol stand to a high-fire-frequency stand that had burned in 4 ofevery 5 years during the past 55 years. Because N stocks and net Nmineralization rates are currently lowest in frequently burned stands,we hypothesized that wood δ15N trajectories would declinethrough time in all burned stands, but at a rate proportional to the firefrequency. We found that wood δ15N records within each standwere remarkably coherent in their mean state and trend through time. Agradual decline in wood δ15N occurred in the mid-20thcentury in the no-, low-, and medium-fire stands, whereas there was notrend in the high-fire stand. The decline in the three stands did notsystematically coincide with the onset of prescribed burning. Thus, wefound limited evidence for variation in wood δ15N that couldbe attributed directly to long-term fire frequency in this prescribedburn experiment in temperate oak savanna. Our wood δ15Nresults may instead reflect decadal-scale changes in vegetationcomposition and abundance due to early- to mid-20th-century firesuppression. 

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5. Chaos in Stochastic 2d Galerkin-Navier–Stokes

   https://doi.org/10.1007/s00220-024-04949-0  

   Bedrossian, Jacob; Punshon-Smith, Sam (April 2024, Communications in Mathematical Physics)

   Abstract We prove that all Galerkin truncations of the 2d stochastic Navier–Stokes equations in vorticity form on any rectangular torus subjected to hypoelliptic, additive stochastic forcing are chaotic at sufficiently small viscosity, provided the frequency truncation satisfies$$N\ge 392$$ $N\ge 392$. By “chaotic” we mean having a strictly positive Lyapunov exponent, i.e. almost-sure asymptotic exponential growth of the derivative with respect to generic initial conditions. A sufficient condition for such results was derived in previous joint work with Alex Blumenthal which reduces the question to the non-degeneracy of a matrix Lie algebra implying Hörmander’s condition for the Markov process lifted to the sphere bundle (projective hypoellipticity). The purpose of this work is to reformulate this condition to be more amenable for Galerkin truncations of PDEs and then to verify this condition using (a) a reduction to genericity properties of a diagonal sub-algebra inspired by the root space decomposition of semi-simple Lie algebras and (b) computational algebraic geometry executed by Maple in exact rational arithmetic. Note that even though we use a computer assisted proof, the result is valid for all aspect ratios and all sufficiently high dimensional truncations; in fact, certain steps simplify in the formal infinite dimensional limit. 

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