PDE models of adder mechanisms in cellular proliferation

Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated with cell division have been proposed. Cells can divide based on the time elapsed since their birth, their size, and/or the volume added since their birth-the timer, sizer, and adder models, respectively. Here, we propose unified adder-sizer models and investigate some of the properties of different adder processes arising in cellular proliferation. Although the adder-sizer model provides a direct way to model cell population structure, we illustrate how it is mathematically related to the well-known model in which cell division depends on age and size. Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities. We then generalize our PDE model to incorporate recent experimental findings of a system exhibiting mother-daughter correlations in cellular growth rates. Numerical experiments illustrating possible average cell volume blowup and the dynamical behavior of cell populations with mother-daughter correlated growth rates are carried out. Finally, motivated by new experimental findings, we extend our adder model cases where the controlling variable is the added size between DNA replication initiation points in the cell cycle

Average-case optimized technology mapping of one-hot domino circuits*

Journal ArticleThis paper presents a technology mapping technique for optimizing the average-case delay of asynchronous combinational circuits implemented using domino logic and one-hot encoded outputs. The technique minimizes the critical path for common input patterns at the possible expense of making less common critical paths longer. To demonstrate the application of this technique, we present a case study of a combinational length decoding block, an integral component of an Asynchronous Instruction Length Decoder (AILD) which can be used in PentiumR processors. The experimental results demonstrate that the average-case delay of our mapped circuits can be dramatically lower than the worst-case delay of the circuits obtained using conventional worst-case mapping techniques

First measurements of high frequency cross-spectra from a pair of large Michelson interferometers

Measurements are reported of the cross-correlation of spectra of differential position signals from the Fermilab Holometer, a pair of co-located 39 m long, high power Michelson interferometers with flat, broadband frequency response in the MHz range. The instrument obtains sensitivity to high frequency correlated signals far exceeding any previous measurement in a broad frequency band extending beyond the 3.8 MHz inverse light crossing time of the apparatus. The dominant but uncorrelated shot noise is averaged down over $2\times 10^8$ independent spectral measurements with 381 Hz frequency resolution to obtain $2.1\times 10^{-20} \ \mathrm{m}/\sqrt{\mathrm{Hz}}$ sensitivity to stationary signals. For signal bandwidths $\Delta f > 11$ kHz, the sensitivity to strain $h$ or shear power spectral density of classical or exotic origin surpasses a milestone $PSD_{\delta h} < t_p$ where $t_p= 5.39\times 10^{-44}/\mathrm{Hz}$ is the Planck time.Comment: 5 pages, 3 figure

Interferometric Constraints on Quantum Geometrical Shear Noise Correlations

Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches for faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.Comment: Matches the journal accepted versio

S=1/2 chains and spin-Peierls transition in TiOCl

We study TiOCl as an example of an S=1/2 layered Mott insulator. From our analysis of new susceptibility data, combined with LDA and LDA+U band structure calculations, we conclude that orbital ordering produces quasi-one-dimensional spin chains and that TiOCl is a new example of Heisenberg-chains which undergo a spin-Peierls transition. The energy scale is an order of magnitude larger than that of previously known examples. The effects of non-magnetic Sc impurities are explained using a model of broken finite chains.Comment: 5 pages, 5 figures (color); details on crystal growth added; to be published in Phys. Rev.

Comparison of single-channel EEG, actigraphy, and sleep diary in cognitively normal and mildly impaired older adults

STUDY OBJECTIVES: Multiple methods for monitoring sleep-wake activity have identified sleep disturbances as risk factors for Alzheimer disease (AD). In order to identify the level of agreement between different methods, we compared sleep parameters derived from single-channel EEG (scEEG), actigraphy, and sleep diaries in cognitively normal and mildly impaired older adults. METHODS: Two hundred ninety-three participants were monitored at home for up to six nights with scEEG, actigraphy, and sleep diaries. Total sleep time (TST), sleep efficiency (SE), sleep onset latency (SOL), and wake after sleep onset (WASO) were calculated using each of these methods. In 109 of the 293 participants, the ratio of cerebrospinal fluid concentrations of phosphorylated tau (p-tau) and amyloid-β-42 (Aβ42) was used as a biomarker for AD pathology. RESULTS: Agreement was highest for TST across instruments, especially in cognitively normal older adults. Overall, scEEG and actigraphy appeared to have greater agreement for multiple sleep parameters than for scEEG and diary or actigraphy and diary. Levels of agreement between scEEG and actigraphy overall decreased in mildly impaired participants and those with biomarker evidence of AD pathology, especially for measurements of TST. CONCLUSIONS: Caution should be exercised when comparing scEEG and actigraphy in individuals with mild cognitive impairment or with AD pathology. Sleep diaries may capture different aspects of sleep compared to scEEG and actigraphy. Additional studies comparing different methods of measuring sleep-wake activity in older adults are necessary to allow for comparison between studies using different methods

Heart rate, startle response, and intrusive trauma memories

The current study adopted the trauma film paradigm to examine potential moderators affecting heart rate (HR) as an indicator of peritraumatic psychological states and as a predictor of intrusive memories. We replicated previous findings that perifilm HR decreases predicted the development of intrusive images and further showed this effect to be specific to images rather than thoughts, and to detail rather than gist recognition memory. Moreover, a group of individuals showing both an atypical sudden reduction in HR after a startle stimulus and higher trait dissociation was identified. Only among these individuals was lower perifilm HR found to indicate higher state dissociation, fear, and anxiety, along with reduced vividness of intrusions. The current findings emphasize how peritraumatic physiological responses relate to emotional reactions and intrusive memory. The moderating role of individual difference in stress defense style was highlighted

Heart rate, startle response, and intrusive trauma memories

Abstract The current study adopted the trauma film paradigm to examine potential moderators affecting heart rate (HR) as an indicator of peritraumatic psychological states and as a predictor of intrusive memories. We replicated previous findings that perifilm HR decreases predicted the development of intrusive images and further showed this effect to be specific to images rather than thoughts, and to detail rather than gist recognition memory. Moreover, a group of individuals showing both an atypical sudden reduction in HR after a startle stimulus and higher trait dissociation was identified. Only among these individuals was lower perifilm HR found to indicate higher state dissociation, fear, and anxiety, along with reduced vividness of intrusions. The current findings emphasize how peritraumatic physiological responses relate to emotional reactions and intrusive memory. The moderating role of individual difference in stress defense style was highlighted

Phase Stability of Lead Phosphate Apatite Pb10−x_{10-x}Cux_{x}(PO4_{4})6_{6}O, Pb10−x_{10-x}Cux_{x}(PO4_{4})6_{6}(OH)2_{2}, and Pb8_{8}Cu2_{2}(PO4_{4})6_{6}

Recently, Cu-substituted lead apatite LK-99 was reported to have room-temperature ambient-pressure superconductivity. Here we utilize density functional theory (DFT) total energy and harmonic phonon calculations to investigate the thermodynamic and dynamic stability of two lead phosphate apatites in their pure and Cu-substituted structures. Though Pb$_{10}$(PO$_4$)$_6$O and Pb$_{10}$(PO$_4$)$_6$(OH)$_2$ are found to be thermodynamically stable (i.e., on the T=0K ground state convex hull), their Cu-substituted counterparts are above the convex hull. Harmonic phonon calculations reveal dynamic instabilities in all four of these structures. Oxygen vacancy formation energies demonstrate that the addition of Cu dopant substituting for Pb increases the likelihood of the formation of oxygen vacancies on the anion site. We propose a new possible phase in this system, Pb$_8$Cu$_2$(PO$_4$)$_6$, where two monovalent Cu atoms are substituted for two Pb(1) atoms and the anion oxygen is removed. We also propose several reaction pathways for Pb$_9$Cu(PO$_4$)$_6$O and Pb$_8$Cu$_2$(PO$_4$)$_6$, and found that both of these two structures are likely to be synthesized under a 1:1 ratio of reactants Pb$_2$SO$_5$ and Cu$_3$P. Our work provides a thorough foundation for the thermodynamic and dynamic stabilities of LK-99 related compounds and we propose several possible novel synthesis reaction pathways and a new predicted structure for future studies