Duty and Distance

Ever since the publication of Peter Singer’s article ‘‘Famine, Affluence, and Morality’’ has the question of whether the (geographical) distance to people in need affects our moral duties towards them been a hotly debated issue. Does geographical distance affect our moral duties? If so, is it of direct moral importance? Or is it of indirect importance to other aspects that affect our moral duties, such as our power to help other people

NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface

An algorithm is derived for computer simulation of geodesics on the constant potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant potential energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to "entropic drift" of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, simulations show that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid

Theories of Fairness and Aggregation

We investigate the issue of aggregativity in fair division problems from the perspective of cooperative game theory and Broomean theories of fairness. Paseau and Saunders (Utilitas 27:460–469, 2015) proved that no non-trivial theory of fairness can be aggregative and conclude that theories of fairness are therefore problematic, or at least incomplete. We observe that there are theories of fairness, particularly those that are based on cooperative game theory, that do not face the problem of non-aggregativity. We use this observation to argue that the universal claim that no non-trivial theory of fairness can guarantee aggregativity is false. Paseau and Saunders’s mistaken assertion can be understood as arising from a neglect of the (cooperative) games approach to fair division. Our treatment has two further pay-offs: for one, we give an accessible introduction to the (cooperative) games approach to fair division, whose significance has hitherto not been appreciated by philosophers working on fairness. For another, our discussion explores the issue of aggregativity in fair division problems in a comprehensive fashion

How to be fairer

We confront the philosophical literature on fair division problems with axiomatic and game-theoretic work in economics. Firstly, we show that the proportionality method advocated in Curtis (in Analysis 74:417–57, 2014) is not implied by a general principle of fairness, and that the proportional rule cannot be explicated axiomatically from that very principle. Secondly, we suggest that Broome’s (in Proc Aristot Soc 91:87–101, 1990) notion of claims is too restrictive and that game-theoretic approaches can rectify this shortcoming. More generally, we argue that axiomatic and game-theoretic work in economics is an indispensable ingredient of any theorizing about fair division problems and allocative justice

Dividing the indivisible: Apportionment and philosophical theories of fairness

Philosophical theories of fairness propose to divide a good that several individuals have a claim to in proportion to the strength of their respective claims. We suggest that currently, these theories face a dilemma when dealing with a good that is indivisible. On the one hand, theories of fairness that use weighted lotteries are either of limited applicability or fall prey to an objection by Brad Hooker. On the other hand, accounts that do without weighted lotteries fall prey to three fairness paradoxes. We demonstrate that division methods from apportionment theory, which has hitherto been ignored by philosophical theories of fairness, can be used to provide fair division for indivisible goods without weighted lotteries and without fairness paradoxes

Entropy-driven phase transition in a polydisperse hard-rods lattice system

We study a system of rods on the 2d square lattice, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N=2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals

Endoplasmic reticulum of rat liver contains two proteins closely related to skeletal sarcoplasmic reticulum Ca-ATPase and calsequestrin.

Rat liver endoplasmic reticulum (ER) membranes were investigated for the presence of proteins having structural relationships with sarcoplasmic reticulum (SR) proteins. Western immunoblots of ER proteins probed with polyclonal antibodies raised against the 100-kDa SR Ca-ATPase of rabbit skeletal muscle identified a single reactive protein of 100 kDa. Also, the antibody inhibited up to 50% the Ca-ATPase activity of isolated ER membranes. Antisera raised against the major intraluminal calcium binding protein of rabbit skeletal muscle SR, calsequestrin (CS), cross-reacted with an ER peptide of about 63 kDa, by the blotting technique. Stains-All treatment of slab gels showed that the cross-reactive peptide stained metachromatically blue, similarly to SR CS. Two-dimensional electrophoresis (Michalak, M., Campbell, K. P., and MacLennan, D. H. (1980) J. Biol. Chem. 255, 1317-1326) of ER proteins showed that the CS-like component of liver ER, similarly to skeletal CS, fell off the diagonal line, as expected from the characteristic pH dependence of the rate of mobility of mammalian CS. In addition, the CS-like component of liver ER was released from the vesicles by alkaline treatment and was found to be able to bind calcium, by a 45Ca overlay technique. From these findings, we conclude that a 100-kDa membrane protein of liver ER is the Ca-ATPase, and that the peripheral protein in the 63-kDa range is closely structurally and functionally related to skeletal CS

Generalized multi-photon quantum interference

Non-classical interference of photons lies at the heart of optical quantum information processing. This effect is exploited in universal quantum gates as well as in purpose-built quantum computers that solve the BosonSampling problem. Although non-classical interference is often associated with perfectly indistinguishable photons this only represents the degenerate case, hard to achieve under realistic experimental conditions. Here we exploit tunable distinguishability to reveal the full spectrum of multi-photon non-classical interference. This we investigate in theory and experiment by controlling the delay times of three photons injected into an integrated interferometric network. We derive the entire coincidence landscape and identify transition matrix immanants as ideally suited functions to describe the generalized case of input photons with arbitrary distinguishability. We introduce a compact description by utilizing a natural basis which decouples the input state from the interferometric network, thereby providing a useful tool for even larger photon numbers