Methods for estimating supersaturation in antisolvent crystallization systems

The mole fraction and activity coefficient-dependent (MFAD) supersaturation expression is the least-assumptive, practical choice for calculating supersaturation in solvent mixtures. This paper reviews the basic thermodynamic derivation of the supersaturation expression, revisits common simplifying assumptions, and discusses the shortcomings of those assumptions for the design of industrial crystallization processes. A step-by-step methodology for estimating the activity-dependent supersaturation is provided with focus on ternary systems. This method requires only solubility data and thermal property data from a single differential scanning calorimetry (DSC) experiment. Two case studies are presented, where common simplifications to the MFAD supersaturation expression are evaluated: (1) for various levels of supersaturation of L-asparagine monohydrate in water–isopropanol mixtures and (2) for the dynamic and steady-state mixed-suspension, mixed-product removal (MSMPR) crystallization of a proprietary API in water–ethanol–tetrahydrofuran solvent mixtures. When compared to the MFAD supersaturation estimation, it becomes clear that errors in excess of 190% may be introduced in the estimation of the crystallization driving force by making unnecessary simplifications to the supersaturation expression. These errors can result in additional parameter regression errors – sometimes by nearly an order of magnitude – for nucleation and growth kinetic parameters, limiting the accurate simulation of dynamic and steady-state crystallization systems

Global and regional left ventricular myocardial deformation measures by magnetic resonance feature tracking in healthy volunteers: comparison with tagging and relevance of gender

This work was funded by a grant from the Engineering and Physical Sciences Research Council (EP/G030693/1) and supported by the Oxford British Heart Foundation Centre of Research Excellence and the National Institute for Health Research Oxford Biomedical Research Centr

High-fidelity readout of trapped-ion qubits

We demonstrate single-shot qubit readout with fidelity sufficient for fault-tolerant quantum computation, for two types of qubit stored in single trapped calcium ions. For an optical qubit stored in the (4S_1/2, 3D_5/2) levels of 40Ca+ we achieve 99.991(1)% average readout fidelity in one million trials, using time-resolved photon counting. An adaptive measurement technique allows 99.99% fidelity to be reached in 145us average detection time. For a hyperfine qubit stored in the long-lived 4S_1/2 (F=3, F=4) sub-levels of 43Ca+ we propose and implement a simple and robust optical pumping scheme to transfer the hyperfine qubit to the optical qubit, capable of a theoretical fidelity 99.95% in 10us. Experimentally we achieve 99.77(3)% net readout fidelity, inferring at least 99.87(4)% fidelity for the transfer operation.Comment: 4 pages, 3 figures; improved readout fidelity (numerical results changed

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Consider a setting where selfish agents are to be assigned to coalitions or projects from a fixed set P. Each project k is characterized by a valuation function; v_k(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: "how should the agents divide the value that they collectively create?". One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.Comment: Under Revie

Structure of Extreme Correlated Equilibria: a Zero-Sum Example and its Implications

We exhibit the rich structure of the set of correlated equilibria by analyzing the simplest of polynomial games: the mixed extension of matching pennies. We show that while the correlated equilibrium set is convex and compact, the structure of its extreme points can be quite complicated. In finite games the ratio of extreme correlated to extreme Nash equilibria can be greater than exponential in the size of the strategy spaces. In polynomial games there can exist extreme correlated equilibria which are not finitely supported; we construct a large family of examples using techniques from ergodic theory. We show that in general the set of correlated equilibrium distributions of a polynomial game cannot be described by conditions on finitely many moments (means, covariances, etc.), in marked contrast to the set of Nash equilibria which is always expressible in terms of finitely many moments

The Phase Diagram of Compact QED Coupled to a Four-Fermi Interaction

Compact lattice Quantum Electrodynamics (QED) with four species of fermions is simulated with massless quarks by using the $\chi$QED scheme of adding a four-fermi interaction to the action. Simulations directly in the chiral limit of massless quarks are done with high statistics on $8^4$, and $16^4$ lattices, and the phase diagram, parameterized by the gauge and the four-fermi couplings, is mapped out. The line of monopole condensation transitions is separate from the line of chiral symmetry restoration. The simulation results indicate that the monopole condensation transition is first order while the chiral transition is second order. The challenges in determining the Universality class of the chiral transition are discussed. If the scaling region for the chiral transition is sufficiently wide, the $16^4$ simulations predict critical indices far from mean field values. We discuss a speculative scenario in which anti-screening provided by double-helix strands of monopole and anti-monopole loops are the agent that balances the screening of fermion anti-fermion pairs to produce an ultra-violet fixed point in the electric coupling.Comment: 29 pages, 8 figures and 2 table

On Budget-Feasible Mechanism Design for Symmetric Submodular Objectives

We study a class of procurement auctions with a budget constraint, where an auctioneer is interested in buying resources or services from a set of agents. Ideally, the auctioneer would like to select a subset of the resources so as to maximize his valuation function, without exceeding a given budget. As the resources are owned by strategic agents however, our overall goal is to design mechanisms that are truthful, budget-feasible, and obtain a good approximation to the optimal value. Budget-feasibility creates additional challenges, making several approaches inapplicable in this setting. Previous results on budget-feasible mechanisms have considered mostly monotone valuation functions. In this work, we mainly focus on symmetric submodular valuations, a prominent class of non-monotone submodular functions that includes cut functions. We begin first with a purely algorithmic result, obtaining a $\frac{2e}{e-1}$-approximation for maximizing symmetric submodular functions under a budget constraint. We view this as a standalone result of independent interest, as it is the best known factor achieved by a deterministic algorithm. We then proceed to propose truthful, budget feasible mechanisms (both deterministic and randomized), paying particular attention on the Budgeted Max Cut problem. Our results significantly improve the known approximation ratios for these objectives, while establishing polynomial running time for cases where only exponential mechanisms were known. At the heart of our approach lies an appropriate combination of local search algorithms with results for monotone submodular valuations, applied to the derived local optima.Comment: A conference version appears in WINE 201

A Comparison of the Notions of Optimality in Soft Constraints and Graphical Games

The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of two formalisms used for different purposes and in different research areas: graphical games and soft constraints. We relate the notion of optimality used in the area of soft constraint satisfaction problems (SCSPs) to that used in graphical games, showing that for a large class of SCSPs that includes weighted constraints every optimal solution corresponds to a Nash equilibrium that is also a Pareto efficient joint strategy

Novel insights into diminished cardiac reserve in non-obstructive hypertrophic cardiomyopathy from four-dimensional flow cardiac magnetic resonance component analysis

Aims: Hypertrophic cardiomyopathy (HCM) is characterized by hypercontractility and diastolic dysfunction, which alter blood flow haemodynamics and are linked with increased risk of adverse clinical events. Four-dimensional flow cardiac magnetic resonance (4D-flow CMR) enables comprehensive characterization of ventricular blood flow patterns. We characterized flow component changes in non-obstructive HCM and assessed their relationship with phenotypic severity and sudden cardiac death (SCD) risk. Methods and results: Fifty-one participants (37 non-obstructive HCM and 14 matched controls) underwent 4D-flow CMR. Left-ventricular (LV) end-diastolic volume was separated into four components: direct flow (blood transiting the ventricle within one cycle), retained inflow (blood entering the ventricle and retained for one cycle), delayed ejection flow (retained ventricular blood ejected during systole), and residual volume (ventricular blood retained for >two cycles). Flow component distribution and component end-diastolic kinetic energy/mL were estimated. HCM patients demonstrated greater direct flow proportions compared with controls (47.9 ± 9% vs. 39.4 ± 6%, P = 0.002), with reduction in other components. Direct flow proportions correlated with LV mass index (r = 0.40, P = 0.004), end-diastolic volume index (r = −0.40, P = 0.017), and SCD risk (r = 0.34, P = 0.039). In contrast to controls, in HCM, stroke volume decreased with increasing direct flow proportions, indicating diminished volumetric reserve. There was no difference in component end-diastolic kinetic energy/mL. Conclusion: Non-obstructive HCM possesses a distinctive flow component distribution pattern characterised by greater direct flow proportions, and direct flow-stroke volume uncoupling indicative of diminished cardiac reserve. The correlation of direct flow proportion with phenotypic severity and SCD risk highlight its potential as a novel and sensitive haemodynamic measure of cardiovascular risk in HCM