Universal Voting Protocol Tweaks to Make Manipulation Hard

Voting is a general method for preference aggregation in multiagent settings, but seminal results have shown that all (nondictatorial) voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where determining a beneficial manipulation is hard computationally. A number of recent papers study the complexity of manipulating existing protocols. This paper is the first work to take the next step of designing new protocols that are especially hard to manipulate. Rather than designing these new protocols from scratch, we instead show how to tweak existing protocols to make manipulation hard, while leaving much of the original nature of the protocol intact. The tweak studied consists of adding one elimination preround to the election. Surprisingly, this extremely simple and universal tweak makes typical protocols hard to manipulate! The protocols become NP-hard, #P-hard, or PSPACE-hard to manipulate, depending on whether the schedule of the preround is determined before the votes are collected, after the votes are collected, or the scheduling and the vote collecting are interleaved, respectively. We prove general sufficient conditions on the protocols for this tweak to introduce the hardness, and show that the most common voting protocols satisfy those conditions. These are the first results in voting settings where manipulation is in a higher complexity class than NP (presuming PSPACE $\neq$ NP)

A microscopic mechanism for rejuvenation and memory effects in spin glasses

Aging in spin glasses (and in some other systems) reveals astonishing effects of `rejuvenation and memory' upon temperature changes. In this paper, we propose microscopic mechanisms (at the scale of spin-spin interactions) which can be at the origin of such phenomena. Firstly, we recall that, in a frustrated system, the effective average interaction between two spins may take different values (possibly with opposite signs) at different temperatures. We give simple examples of such situations, which we compute exactly. Such mechanisms can explain why new ordering processes (rejuvenation) seem to take place in spin glasses when the temperature is lowered. Secondly, we emphasize the fact that inhomogeneous interactions do naturally lead to a wide distribution of relaxation times for thermally activated flips. `Memory spots' spontaneously appear, in the sense that the flipping time of some spin clusters becomes extremely long when the temperature is decreased. Such memory spots are capable of keeping the memory of previous ordering at a higher temperature while new ordering processes occur at a lower temperature. After a qualitative discussion of these mechanisms, we show in the numerical simulation of a simplified example that this may indeed work. Our conclusion is that certain chaos-like phenomena may show up spontaneously in any frustrated and inhomogeneous magnetic system, without impeding the occurrence of memory effects.Comment: 9 pages (11 figures) - revised version, to appear in Eur. Phys. J. B (2001

Effective theory of excitations in a Feshbach resonant superfluid

A strongly interacting Fermi gas, such as that of cold atoms operative near a Feshbach resonance, is difficult to study by perturbative many-body theory to go beyond mean field approximation. Here I develop an effective field theory for the resonant superfluid based on broken symmetry. The theory retains both fermionic quasiparticles and superfluid phonons, the interaction between them being derived non-perturbatively. The theory converges and can be improved order by order, in a manner governed by a low energy expansion rather than by coupling constant. I apply the effective theory to calculate the specific heat and propose a mechanism of understanding the empirical power law of energy versus temperature recently measured in a heat capacity experiment.Comment: 4+ pages, 1 figure; Added references, corrected and clarified minor statements (v.2

The Cauchy Operator for Basic Hypergeometric Series

We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2\phi_1$ transformation formula and Sears' ${}_3\phi_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator $T(bD_q)$. Using this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy integral, Sears' two-term summation formula, as well as the $q$-analogues of Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big $q$-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic

Non-equilibrium Green's function theory for non-adiabatic effects in quantum transport: inclusion of electron-electron interactions

Non-equilibrium Green's function theory for non-adiabatic effects in quantum transport [Kershaw and Kosov, J.Chem. Phys. 2017, 147, 224109 and J. Chem. Phys. 2018, 149, 044121] is extended to the case of interacting electrons. We consider a general problem of quantum transport of interacting electrons through a central region with dynamically changing geometry. The approach is based on the separation of time scales in the non-equilibrium Green's functions and the use of Wigner transformation to solve the Kadanoff-Baym equations. The Green's functions and correlation self-energy are non-adiabatically expanded up to the second order central time derivatives. We produced expressions for Green's functions with non-adiabatic corrections and modified formula for electric current; both depend not only on instantaneous molecular junction geometry but also on nuclear velocities and accelerations. The theory is illustrated by the study of electron transport through a model single-resonant level molecular junction with local electron-electron repulsion and a dynamically changing geometry

Nonadiabatic corrections to electric current in molecular junction due to nuclear motion at the molecule-electrode interfaces

We present quantum electron transport theory that incorporates dynamical effects of motion of atoms on electrode-molecule interfaces in the calculations of the electric current. The theory is based on non-equilibrium Green's functions. We separate time scales in the Green's functions on fast relative time and slow central time. The derivative with respect to the central time serves as a small parameter in the theory. We solve the real-time Kadanoff-Baym equations for molecular Green's functions using Wigner representation and keep terms up to the second order with respect to the central time derivatives. Molecular Green's functions and consequently the electric current are expressed as functions of molecular junction coordinates as well as velocities and accelerations of molecule-electrode interface nuclei. We apply the theory to model a molecular system and study the effects of non-adiabatic nuclear motion on molecular junction conductivity

Lithium : old & new uses in medicine

Lithium has been used in psychiatry since 1949, and since the mid 1960s its use has escalated until it is estimated that about 500,000 patients receive it world-wide. During the last decade a new phase of interest in lithium has begun. Lithium is being used with beneficial effects as a treatment in other health related problems unrelated to psychiatry.peer-reviewe