Approximate Proportionality Research Articles

Welfare Maximization in Perpetual Voting (Student Abstract)

We study the computational problems associated with maximizing various welfare objectives—namely utilitarian welfare, egalitarian welfare, and Nash welfare—in perpetual voting, a sequential collective decision-making framework. Prior work look into notions of fairness over time and study extensions of single-round voting rules to the multi-round setting. We show that while a utilitarian-welfare maximizing outcome can be computed efficiently, an outcome that maximizes egalitarian or Nash welfare is computationally intractable, even in the case of two candidates. We complement this by showing that maximizing egalitarian welfare is fixed-parameter tractable in the number of agents, and maximizing egalitarian or Nash welfare is W[2]-hard and slicewise polynomial in the number of timesteps. We also provide an approximation algorithm for maximizing egalitarian welfare and study strategyproofness with respect to these welfare objectives. Finally, we show that a simple greedy algorithm can achieve approximate proportionality in this setting.

Insights into the feature size required for the death of Pseudomonas fluorescens on nanostructured silicon fabricated by block copolymer lithography

It has been established that nanostructured surfaces can cause cell death for Gram-negative species; however, the exact mode of action has not yet been determined from among several agreed-upon possibilities. Herein, silicon nanospike arrays were fabricated via a combination of block copolymer lithography and plasma etching. Patterns were first developed on silicon substrates using tetrahydrofuran, chloroform, or acetic acid as annealing solvents with two different molecular weight block copolymers. Three silicon surface types (NSS, NSM and NSL) were fabricated after a hard mask development and plasma etching. These samples were designed to be “small, medium and large” versions of nanospike arrays regarding their height, diameter and pitch; maintaining the same approximate proportionality, while changing in size. NSS had structures of 28 nm in height, and 16 nm in base diameter, with a pitch of 36 nm. NSM structures were 140 nm in height, and 31 nm in diameter, with a pitch of 63 nm. NSL surface structures had a height of 272 nm, a diameter of 47 nm and a pitch of 99 nm. When suspensions of gentamicin-resistant P. fluorescens cells were interfaced with the arrays for 24 h, it was shown that the NSS had ∼76% less cell death than both NSM and NSL. To the best of our knowledge, this is the first study that etched silicon patterned using block copolymer lithography has been used to fabricate surfaces with antibacterial activity.

Preliminary Safety, Pharmacological and Efficacy Data from Patients with Relapsed or Refractory B-Cell Malignancies Treated with the ICP-248, a Next Generation BCL2 Inhibitor

Background: BCL2, a key protein regulator of the apoptotic pathway, is constitutively expressed in various malignancies, which is a hallmark of cancer cell. BCL2 inhibitors have been shown to be safe and effective and are approved for the treatment of patients with chronic lymphocytic leukemia/small cell lymphoma (CLL/SLL) or acute myeloid leukemia (AML). Venetoclax, the first and only approved BCL2 inhibitor, is associated with gastrointestinal toxicities and tumor lysis syndrome (TLS). Therefore, ICP-248 was developed as a potent and highly selective inhibitor of BCL2 and has shown antitumor activity superior to venetoclax in preclinical studies. Preclinical studies of ICP-248 have demonstrated favorable pharmacokinetics profile, broad safety window and excellent safety profile, as well as synergistic effect in anti-tumor activity in combination with Orelabrutinib, a novel and highly selective BTK inhibitor. Methods: ICP-CL-1201 is a phase I study to evaluate the safety, tolerability, pharmacokinetics, pharmacodynamics, and preliminary efficacy of ICP-248 in patients with relapsed or refractory B-cell malignancies ( ClinicalTrials.gov ID: NCT05728658). The study will be conducted in 2 parts. Part 1 will evaluate ICP-248 as monotherapy at the target dose of 100mg, 200mg, 300mg, 400mg, 500mg and 600mg (once daily and 28 days per cycle) and will explore different ramp-up dosing strategies. Part 2 will evaluate ICP-248 in selected and proposed indications. The dose escalation in Part 1 will follow the 3+3 design with dose-limiting toxicity (DLT) observation window with 49 days. Eligible patients include those with CLL/SLL and B-cell non-Hodgkin lymphomas (NHLs) who failed on available therapy. Key exclusion criteria include CNS involvement, prior exposure to BCL2 inhibitors and clinically significant cardiovascular disease. Adverse events (AEs) are reported per common terminology criteria for AEs (CTCAE) v5.0. Efficacy was evaluated according to the Lugano 2014 or International Workshop on Chronic Lymphocytic Leukemia (iwCLL) 2018 criteria. Minimal residual disease was evaluated with flow or next generation sequencing. Results: As of 30 th July, 2023 (data cutoff date) 3 patents (mantle cell lymphoma [MCL], SLL and CLL) had been enrolled at the dose level of 100 mg QD; age ranging from 53 to 68; follow-up ranging from 1.9 to 4.7 months); median of prior regimen numbers was 3 (range, 1-3; 2 out 3 patients failed on zanubrutinib or pirtobrutinib). ICP-248 demonstrated a favorable PK profile, approximate dose proportionality was observed across the ramp-up stage. No DLTs and SAEs were observed. All the AEs were grade 1 to 2 (mainly neutropenia) without dose interruption and modifications. No TLS including laboratory TLS was observed. Two patients with MCL and SLL were assessed as complete response (CR) at the end of cycle 2, and the CLL patient was assessed as stable disease without sign and symptom of disease and recovering hematology. Undetectable MRD was confirmed in the patient with SLL and MCL. Conclusions: Preliminary results suggest that ICP-248 is safe and well tolerated in relapsed or refractory B-cell malignancies. The favorable clinical pharmacological and safety profiles support current dose ramp up strategy. Preliminary efficacy data demonstrated good response with deep remission. Further assessment of safety and efficacy with additional dose levels and dosing strategies will be pursued in expanded patient population and in the combination with orelabrutinib.

Differentially Private Fair Division

Fairness and privacy are two important concerns in social decision-making processes such as resource allocation. We study privacy in the fair allocation of indivisible resources using the well-established framework of differential privacy. We present algorithms for approximate envy-freeness and proportionality when two instances are considered to be adjacent if they differ only on the utility of a single agent for a single item. On the other hand, we provide strong negative results for both fairness criteria when the adjacency notion allows the entire utility function of a single agent to change.

Allometry of the quasi-pipe (qPipe) model for estimating tree leaf area and tree leaf mass applied to plant functional types

The allometry of the pipe model quantifies the approximate proportionality between the tree leaf amount and the stem cross-sectional area at the crown base (ACB). It is useful for estimating and modeling carbon fixation abilities of trees but requires climbing the tree and is thus unsuitable for large-scale studies. Here, we adopted a previously proposed allometry (hereafter the quasi-pipe (qPipe) model allometry) formulating the relationship between the tree leaf amount and a surrogate of ACB, ACB_Est, calculated from tree dimensions measurable from the ground. Using published/unpublished data for 962 trees of 159 species collected between tropical rainforests and boreal forests, we established pipe and qPipe model allometries for evergreen-conifer, deciduous-conifer, evergreen-broadleaf, and deciduous-broadleaf plant functional types (PFTs). For the leaf area per tree (LA), allometric lines on a log–log plane were almost identical among the four PFTs in both models, with slopes of ~ 1. For the leaf mass per tree (LM), however, the allometric lines separated among the four PFTs in both models and had slopes greater than 1, indicating that the proportionality assumed in the pipe model held for LA but not LM. The applicability of the qPipe model in estimating the stand-scale leaf amount was further examined.

On existence of truthful fair cake cutting mechanisms

We study the fair division problem on divisible heterogeneous resources (the cake cutting problem) with strategic agents, where each agent can manipulate his/her private valuation to receive a better allocation. A (direct-revelation) mechanism takes agents' reported valuations as input and outputs an allocation that satisfies a given fairness requirement. A natural and fundamental open problem, first raised by Chen, Lai, Parkes, and Procaccia [1] and subsequently raised in reference [2–7], etc., is whether there exists a deterministic, truthful, and envy-free (or even proportional) cake cutting mechanism. In this paper, we resolve this open problem by proving that there does not exist a deterministic, truthful and proportional cake cutting mechanism, even in the special case where all of the following hold:•there are only two agents;•each agent's valuation is a piecewise-constant function;•each agent is hungry: each agent has a strictly positive value on any part of the cake. The impossibility result extends to the case where the mechanism is allowed to leave some part of the cake unallocated.We also present a truthful and envy-free mechanism when each agent's valuation is piecewise-constant and monotone. However, if we require Pareto-optimality, we show that truthful is incompatible with approximate proportionality for any positive approximation ratio even for piecewise-constant and monotone value density functions.To circumvent the main impossibility result, we aim to design mechanisms that possess a certain degree of truthfulness. Motivated by the kind of truthfulness possessed by the classical I-cut-you-choose protocol, we propose a weaker notion of truthfulness, the proportional risk-averse truthfulness. We show that the well-known moving-knife (Dubins-Spanier) procedure and Even-Paz algorithm do not have this truthful property. We propose a mechanism that is proportionally risk-averse truthful and envy-free, and a mechanism that is proportionally risk-averse truthful that always outputs allocations with connected pieces.

Efficacy, Safety and Pharmacokinetics of IL-17 Monoclonal Antibody Injection (AK111) in Patients with Moderate-to-Severe Plaque Psoriasis: A Randomized, Double-Blinded, Placebo-Controlled Phase Ib Multidose Escalation Clinical Study.

To evaluate the safety, tolerability, immunogenicity, and induced expression of skin biomarkers of AK111 injection after multiple administrations in subjects with moderate-to-severe plaque psoriasis. This study is a randomized, double-blinded, placebo-parallel-controlled study using a dose escalation mode of multiple doses. A total of 48 subjects were sequentially randomized to receive each AK111 dose regimen (75mg, 150mg, 300mg, 450mg) or the corresponding placebo. All subjects were treated with the study drug at weeks0, 1, 4, and 8 and were unblinded at week 12, with the placebo group ending and the AK111 group being followed up to 20weeks. At week12, compared with placebo, the percentage of subjects achieving Psoriasis Area and Severity Index 75 (PASI75) and static Physician Global Assessment (sPGA) 0/1 in the AK111 75mg-450mg dose groups was significantly increased, and higher PASI90 was achieved in the 150mg, 300mg, and 450mg dose groups than in the 75mg group. All efficacy indicators were maintained at week 20. The incidence of treatment-emergent anti-drugantibodies (ADAs) was 0% (0/48). Neutralizing antibodies (NAbs) were not detected in any subject. The proportion of subjects who reported any treatment-emergent adverse event (TEAE) was 75.0% in the AK111 group, similar to the 66.7% in the placebo group. The most commonly reported adverse events were hyperglycemia, elevated blood pressure, and hypokalemia. The AK111 pharmacokinetics showed approximate dose proportionality with regard to the maximum observed concentration (Cmax) and area under the curve from 0 to the time of the last quantifiable concentration (AUC0-t) following subcutaneous injection doses of 150-450mg. After moderate-to-severe plaque psoriasis subjects received multiple subcutaneous AK111 injections of 150-450mg, AK111 exposure increased in a roughly dose-proportional relationship. AK111 was safe and tolerable. In subjects with moderate-to-severe plaque psoriasis, AK111 demonstrated encouraging preliminary efficacy, which was sustained for a relatively long time after the last dose administration. The clinical trial identification number is NCT05504317.

Experimental investigation of aluminum-air burning velocity at elevated pressure

Aluminum is an energy-dense metal that reacts exothermically with a range of oxidizers, making it a potentially useful fuel for certain thermal energy and power applications (e.g., boilers, swirl-stabilized burners, rockets, etc.). In addition to its reactive properties, aluminum is naturally abundant and commercially available in fine powders that are relatively inexpensive and chemically stable. Fine aluminum dusts, with particle diameters on the order of micrometers, can be aerosolized and mixed with a gaseous oxidizer such as air to create stable dust flames and heat for a thermodynamic cycle. In order to realize the potential utility of aluminum-air dust flames, the fundamental combustion behavior, such as the burning velocity, must be understood. In this work, an experimental system was developed that allows metal dust flames to be observed within an optically-accessible pressurized chamber. Using a high-speed camera, fuel-rich premixed aluminum-air jet flames were imaged through narrowband interference filters, and the data were used to calculate burning velocity. A single polydisperse size distribution of particles was tested at pressures ranging from 1 to 7.2 bar. Burning velocity was found to decrease with increased pressure (P), with an approximate proportionality to P−0.6 over the range of pressures tested (∼P−0.3 for only the laminar flow conditions). This reduction in burning velocity with increased pressure is hypothesized to occur due to increased oxidizer density along with a decrease in interparticle spacing, which may result in asymmetric particle heating and increased competition for oxidizer.

INFLUENCE OF SOLUTIONS OF DIFFERENT OSMOLARITY ON MORPHOMETRIC PARAMETERS OF 15-32-CELLS BOVINE EMBRYOS

The illustrative material was obtained that allows to observe clearly the effect of different tonicity solutions on the morphology of bovine 5-days pre-compacted 15-17-cells embryos and 6-days early morulae obtained in vivo, depending on their technological state. The average values and rates of variation of the following morphometric parameters were determined in embryos at the stages of the developmental study: outer and inner zona pellucida (ZP) diameters, ZP thickness, embryonic cell mass (CM) diameter and individual embryonic cell diameters. The mentioned parameters were determined in each of the embryos consistently in intact, denuded and deblastomerised states in isotonic (0.29 Osm), hypertonic (1.5 Osm) and hypotonic (0.2 Osm) conditions. Manipulations with embryos were carried out in such a way that during consistent transfer through solutions of different osmolarity, it was possible to identify the dynamics of changes in the morphology and parameters of each of the embryos (in the intact state and after denudation) and of each of the individual embryonic cells (after deblastomerisation of the embryo). A decrease or increase in the size of the CM of embryos of the studied developmental stages during their successive transfer through solutions with different osmolarity occurred with the preservation of the approximate proportionality of their shape. After partial dehydration in hypertonia, the denuded embryos recovered their sizes mostly not fully relative to their initial sizes in the intact state in solutions of the appropriate osmolarity. Similar osmotic behavior was also observed in individual cells of deblastomerised embryos. The experimental data presented in the article make it possible to predict the behavior of embryos during micromanipulations, to determine the sequence, technique and conditions of operations with them, as well as the types, shape and sizes of microtools necessary for this.

ЕЛЕКТРОМАГНІТНІ ЕФЕКТИ АКУСТИКО-ГРАВІТАЦІЙНИХ ХВИЛЬ У ПРИЗЕМНІЙ АТМОСФЕРІ

Purpose: Acoustic and atmospheric gravity waves (AAGW) are generated by many natural and anthropogenic sources. The AAGW propagation at ionospheric heights is accompanied by the generation of disturbances in the magnetic and electric fields. The plasma presence plays a crucial role. The mechanisms for generating electrical and magnetic disturbances in the near-Earth atmosphere by the AAGW have been studied much worse. Therefore, the validation of the capability to generate electromagnetic disturbances in the near-Earth atmosphere by the AAGW is an urgent problem. The purpose of this paper is to describe the mechanism for generating disturbances in the electric and magnetic fields in the near-Earth atmosphere under the action of AAGW and to estimate the amplitudes of these disturbances for various AAGW sources. Design/methodology/approach: The impact of a series of highenergy sources often results in the generation of synchronous disturbances in the acoustic and geoelectric (atmospheric) fields, when an approximate proportionality between the pressure amplitude and the amplitude of the disturbances in the atmospheric electric field is observed to occur. Based on the observational data and making use of the Maxwell equations, the theoretical estimates of the disturbances in the electric and magnetic fields have been obtained. Findings: Simplified expressions have been obtained for estimating the amplitudes of the electric and magnetic fields under the action of the AAGW generated by natural and manmade sources. The amplitudes of the electric and magnetic fields generated by the AAGW of natural and manmade origin, which travel in the near-Earth atmosphere, have been calculated. The amplitudes of the AAGW generated electric and magnetic fields are shown to be large enough to be detected with the existing electrometers and fluxmeter magnetometers. The magnitudes of the amplitudes of the electric and magnetic fields generated in the near-Earth atmosphere under the action of AAGW are large enough to trigger coupling between the subsystems in the Earth–atmosphere–ionosphere–magnetosphere system. Conclusions: The estimates and not numerous observations are in good agreement. Key words: acoustic and atmospheric gravity waves, near-Earth atmosphere, volume charge, atmospheric pressure disturbances, electric field, magnetic field

Secondary Ice Production by Fragmentation of Freezing Drops: Formulation and Theory

Abstract A numerical formulation is provided for secondary ice production during fragmentation of freezing raindrops or drizzle. This is obtained by pooling laboratory observations from published studies and considering the physics of collisions. There are two modes of the scheme: fragmentation during spherical drop freezing (mode 1) and during collisions of supercooled raindrops with more massive ice (mode 2). The empirical scheme is for atmospheric models. Microphysical simulations with a parcel model of fast ascent (8 m s−1) between −10° and −20°C are validated against aircraft observations of tropical maritime deep convection. Ice enhancement by an order of magnitude is predicted from inclusion of raindrop-freezing fragmentation, as observed. The Hallett–Mossop (HM) process was active too. Both secondary ice mechanisms (HM and raindrop freezing) are accelerated by a positive feedback involving collisional raindrop freezing. An energy-based theory is proposed explaining the laboratory observations of mode 1, both of approximate proportionality between drop size and fragment numbers and of their thermal peak. To illustrate the behavior of the scheme in both modes, the glaciation of idealized monodisperse populations of drops is elucidated with an analytical zero-dimensional (0D) theory treating the freezing in drop–ice collisions by a positive feedback of fragmentation. When drops are too few or too small (≪1 mm), especially at temperatures far from −15°C (mode 1), there is little raindrop-freezing fragmentation on realistic time scales of natural clouds, but otherwise, high ice enhancement (IE) ratios of up to 100–1000 are possible. Theoretical formulas for the glaciation time of such drop populations, and their maximum and initial growth rates of IE ratio, are proposed.

Pharmacokinetics, Pharmacodynamics, and Tolerability of Single-Dose Oral LCB01-0371, a Novel Oxazolidinone with Broad-Spectrum Activity, in Healthy Volunteers.

LCB01-0371 is a novel oxazolidinone with broad-spectrum activity against Gram-positive pathogens in both in vitro studies and animal infection models. The objectives of this study were to evaluate its safety, tolerability, pharmacokinetics, and pharmacodynamics following single ascending doses. Single oral doses of 600 mg linezolid, a placebo, or LCB01-0371 of between 50 mg and 3,200 mg were tested in 69 healthy male subjects. Blood and urine were sampled, LCB01-0371 concentrations were measured, and the serum inhibitory and bactericidal titers of LCB01-0371 and linezolid were determined. LCB01-0371 was well tolerated up to 2,400 mg. The most common drug-related clinical and laboratory adverse events were nausea with or without vomiting, decreased neutrophil counts, and increased total bilirubin levels. The frequency of adverse events and drug-related adverse events was similar among the treatment groups. The systemic exposure was approximately dose proportional over the range of 50 mg to 800 mg, which includes the anticipated clinical dose. The mean clearance, renal clearance, and volume of distribution were significantly decreased at higher doses (above 800 mg). LCB01-0371 exhibited early bacteriostatic activity against all tested strains except for Streptococcus pneumoniae strains, and the potency of LCB01-0371 at 800 mg was similar to that of linezolid at the therapeutic dose (600 mg). However, LCB01-0371 had less bactericidal activity than linezolid. Taken together, LCB01-0371 was well tolerated, exhibited approximate dose proportionality within the anticipated clinically relevant dose range, and showed bacteriostatic and bactericidal activity comparable to that of linezolid. These results support the further clinical development of LCB01-0371. (This study has been registered at ClinicalTrials.gov under registration no. NCT01554995.).

Calculation of Chemical Shifts of X-Ray-Emission Spectra of Niobium in Niobium(V) Oxides Relative to Metal

Chemical shifts of the Kα1 and Kβ1 lines of X-ray-emission spectra of niobium in oxides (Nb2O5)n, n = 1–4, relative to metal Nb have been calculated. Stoichiometric clusters (Nb2O5)n the electronic structure of which was calculated using accurate relativistic pseudopotentials and two-component version of the density functional theory are considered as prototypes for modeling different crystal forms of niobium(V) oxide. The chemical shifts were calculated using the method based on using the property of approximate proportionality of valence spinors in the core region of the heavy atom [11]. Corrections to values of chemical shifts have been determined with allowance for deviations from the abovementioned proportionality. Rapid convergence of results with respect to the size of the niobium oxide cluster has been demonstrated.

A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 1: Frequency analysis

Abstract. We develop a general framework for the frequency analysis of irregularly sampled time series. It is based on the Lomb–Scargle periodogram, but extended to algebraic operators accounting for the presence of a polynomial trend in the model for the data, in addition to a periodic component and a background noise. Special care is devoted to the correlation between the trend and the periodic component. This new periodogram is then cast into the Welch overlapping segment averaging (WOSA) method in order to reduce its variance. We also design a test of significance for the WOSA periodogram, against the background noise. The model for the background noise is a stationary Gaussian continuous autoregressive-moving-average (CARMA) process, more general than the classical Gaussian white or red noise processes. CARMA parameters are estimated following a Bayesian framework. We provide algorithms that compute the confidence levels for the WOSA periodogram and fully take into account the uncertainty in the CARMA noise parameters. Alternatively, a theory using point estimates of CARMA parameters provides analytical confidence levels for the WOSA periodogram, which are more accurate than Markov chain Monte Carlo (MCMC) confidence levels and, below some threshold for the number of data points, less costly in computing time. We then estimate the amplitude of the periodic component with least-squares methods, and derive an approximate proportionality between the squared amplitude and the periodogram. This proportionality leads to a new extension for the periodogram: the weighted WOSA periodogram, which we recommend for most frequency analyses with irregularly sampled data. The estimated signal amplitude also permits filtering in a frequency band. Our results generalise and unify methods developed in the fields of geosciences, engineering, astronomy and astrophysics. They also constitute the starting point for an extension to the continuous wavelet transform developed in a companion article (Lenoir and Crucifix, 2018). All the methods presented in this paper are available to the reader in the Python package WAVEPAL.

Lepton universality violation and right-handed currents in b → cτν

We consider the recent LHCb result for Bc→J/ψτν in conjunction with the existing anomalies in R(D) and R(D⋆) within the framework of a right-handed current with enhanced couplings to the third generation. The model predicts a linear relation between the observables and their SM values in terms of two combinations of parameters. The strong constraints from b→sγ on W−W′ mixing effectively remove one of the combinations of parameters resulting in an approximate proportionality between all three observables and their SM values. To accommodate the current averages for R(D) and R(D⋆), the W′ mass should be near 1 TeV, and possibly accessible to direct searches at the LHC. In this scenario we find that R(J/ψ) is enhanced by about 20% with respect to its SM value and about 1.5σ below the central value of the LHCb measurement. The predicted dΓ/dq2 distribution for B→D(D⋆)τν is in agreement with the measurement and the model satisfies the constraint from the Bc lifetime.

Recombinant ADAMTS-13: first-in-human pharmacokinetics and safety in congenital thrombotic thrombocytopenic purpura

AbstractSafety, tolerability, and pharmacokinetics of recombinant ADAMTS-13 (a disintegrin and metalloproteinase with a thrombospondin type 1 motif, member 13; BAX 930; SHP655) were investigated in 15 patients diagnosed with severe congenital ADAMTS-13 deficiency (plasma ADAMTS-13 activity <6%) in a prospective phase 1, first-in-human, multicenter dose escalation study. BAX 930 was well tolerated, no serious adverse events occurred, and no anti-ADAMTS-13 antibodies were observed. After single-dose administration of BAX 930 at 5, 20, or 40 U/kg body weight to adolescents and adults, there was approximate dose proportionality with respect to maximum plasma concentration (Cmax [U/mL]) and area under the concentration–time curve (AUC [h∙U/mL]). Dose-related increases of individual ADAMTS-13:Ag and activity were observed and reached a maximum within 1 hour. With escalating BAX 930 doses administered, a dose-dependent persistence of ADAMTS-13-mediated von Willebrand factor (VWF) cleavage products and reduced VWF multimeric size were observed. This study demonstrated that pharmacokinetic parameters of BAX 930 were comparable to those estimated in previous plasma infusion studies and provided evidence of pharmacodynamic activity. This study was registered at www.clinicaltrials.gov as #NCT02216084.

Origin of path independence between cumulative CO $$_{2}$$ 2 emissions and global warming

Observations and GCMs exhibit approximate proportionality between cumulative carbon dioxide (CO $$_{2}$$ ) emissions and global warming. Here we identify sufficient conditions for the relationship between cumulative CO $$_{2}$$ emissions and global warming to be independent of the path of CO $$_{2}$$ emissions; referred to as “path independence”. Our starting point is a closed form expression for global warming in a two-box energy balance model (EBM), which depends explicitly on cumulative emissions, airborne fraction and time. Path independence requires that this function can be approximated as depending on cumulative emissions alone. We show that path independence arises from weak constraints, occurring if the timescale for changes in cumulative emissions (equal to ratio between cumulative emissions and emissions rate) is small compared to the timescale for changes in airborne fraction (which depends on CO $$_{2}$$ uptake), and also small relative to a derived climate model parameter called the damping-timescale, which is related to the rate at which deep-ocean warming affects global warming. Effects of uncertainties in the climate model and carbon cycle are examined. Large deep-ocean heat capacity in the Earth system is not necessary for path independence, which appears resilient to climate modeling uncertainties. However long time-constants in the Earth system carbon cycle are essential, ensuring that airborne fraction changes slowly with timescale much longer than the timescale for changes in cumulative emissions. Therefore path independence between cumulative emissions and warming cannot arise for short-lived greenhouse gases.

Shared dynamical features of smooth- and rough-wall boundary-layer turbulence

The structure of smooth- and rough-wall turbulent boundary layers is investigated using existing data and newly acquired measurements derived from a four element spanwise vorticity sensor. Scaling behaviours and structural features are interpreted using the mean momentum equation based framework described for smooth-wall flows by Klewicki (J. Fluid Mech., vol. 718, 2013, pp. 596–621), and its extension to rough-wall flows by Mehdiet al.(J. Fluid Mech., vol. 731, 2013, pp. 682–712). This framework holds potential relative to identifying and characterizing universal attributes shared by smooth- and rough-wall flows. As prescribed by the theory, the present analyses show that a number of statistical features evidence invariance when normalized using the characteristic length associated with the wall-normal transition to inertial leading-order mean dynamics. On the inertial domain, the spatial size of the advective transport contributions to the mean momentum balance attain approximate proportionality with this length over significant ranges of roughness and Reynolds number. The present results support the hypothesis of Mehdiet al., that outer-layer similarity is, in general, only approximately satisfied in rough-wall flows. This is because roughness almost invariably leaves some imprint on the vorticity field; stemming from the process by which roughness influences (generally augments) the near-wall three-dimensionalization of the vorticity field. The present results further indicate that the violation of outer similarity over regularly spaced spanwise oriented bar roughness correlates with the absence of scale separation between the motions associated with the wall-normal velocity and spanwise vorticity on the inertial domain.

The evolution of high-redshift massive black holes

AbstractMassive black holes (MBHs) are nowadays recognized as integral parts of galaxy evolution. Both the approximate proportionality between MBH and galaxy mass, and the expected importance of feedback from active MBHs in regulating star formation in their host galaxies point to a strong interplay between MBHs and galaxies. MBHs must form in the first galaxies and be fed by gas in these galaxies, with continuous or intermittent inflows that, at times, can be larger than the Eddington rate. Feedback from supernovae and from the MBHs themselves modulates the growth of the first MBHs. While current observational data only probe the most massive and luminous MBHs, the tip of the iceberg, we will soon be able to test theoretical models of MBH evolution on more “normal” MBHs: the MBHs that are indeed relevant in building the population that we observe in local galaxies, including our own Milky Way.

Adding high time resolution to charge-state-specific ion energy measurements for pulsed copper vacuum arc plasmas

Charge-state-resolved ion energy–time distributions of pulsed Cu arc plasma were obtained by using direct (time-dependent) acquisition of the ion detection signal from a commercial ion mass-per-charge and energy-per-charge analyzer. We find a shift of energies of Cu2+, Cu3+ and Cu4+ ions to lower values during the first few hundred microseconds after arc ignition, which is evidence for particle collisions in the plasma. The generation of Cu+ ions in the later part of the pulse, measured by the increase of Cu+ signal intensity and an associated slight reduction of the mean charge state, points to charge exchange reactions between ions and neutrals. At the very beginning of the pulse, when the plasma expands into vacuum and the plasma potential strongly fluctuates, ions with much higher energy (over 200 eV) are observed. Early in the pulse, the ion energies observed are approximately proportional to the ion charge state, and we conclude that the acceleration mechanism is primarily based on acceleration in an electric field. This field is directed away from the cathode, indicative of a potential hump. Measurements by a floating probe suggest that potential structures travel, and ions moving in the traveling field can gain high energies up to a few hundred electron-volts. Later in the pulse, the approximate proportionality is lost, which is related to increased smearing out of different energies due to collisions with neutrals, and/or to a change of the acceleration character from electrostatic to ‘gas-dynamic’, i.e. dominated by pressure gradient.