TY - JOUR
AB - We use the dual boson approach to reveal the phase diagram of the Fermi-Hubbard model with long-range dipole-dipole interactions. By using a large-scale finite-temperature calculation on a 64×64 square lattice we demonstrate the existence of a novel phase, possessing an "ultralong-range" order. The fingerprint of this phase - the density correlation function - features a nontrivial behavior on a scale of tens of lattice sites. We study the properties and the stability of the ultralong-range-ordered phase, and show that it is accessible in modern experiments with ultracold polar molecules and magnetic atoms.
AU - Van Loon, Erik
AU - Katsnelson, Mikhail
AU - Lemeshko, Mikhail
ID - 1700
IS - 8
JF - Physical Review B
TI - Ultralong-range order in the Fermi-Hubbard model with long-range interactions
VL - 92
ER -
TY - JOUR
AB - The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance.
AU - Tkacik, Gasper
AU - Mora, Thierry
AU - Marre, Olivier
AU - Amodei, Dario
AU - Palmer, Stephanie
AU - Berry Ii, Michael
AU - Bialek, William
ID - 1701
IS - 37
JF - PNAS
TI - Thermodynamics and signatures of criticality in a network of neurons
VL - 112
ER -
TY - JOUR
AB - Given a convex function (Formula presented.) and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691–705, 2014) the relative entropy defined by (Formula presented.). Among other things, they prove that the so-defined quantity is monotone if and only if (Formula presented.) is operator monotone. The monotonicity is then used to properly define (Formula presented.) for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections (Formula presented.) with (Formula presented.) strongly, the limit (Formula presented.) is shown to exist and to be independent of the sequence of projections (Formula presented.). The question whether this sequence converges to its "obvious" limit, namely (Formula presented.), has been left open. We answer this question in principle affirmatively and show that (Formula presented.). If the operators A and B are regular enough, that is (A − B), (Formula presented.) and (Formula presented.) are trace-class, the identity (Formula presented.) holds.
AU - Deuchert, Andreas
AU - Hainzl, Christian
AU - Seiringer, Robert
ID - 1704
IS - 10
JF - Letters in Mathematical Physics
TI - Note on a family of monotone quantum relative entropies
VL - 105
ER -
TY - CONF
AB - We consider a problem of learning kernels for use in SVM classification in the multi-task and lifelong scenarios and provide generalization bounds on the error of a large margin classifier. Our results show that, under mild conditions on the family of kernels used for learning, solving several related tasks simultaneously is beneficial over single task learning. In particular, as the number of observed tasks grows, assuming that in the considered family of kernels there exists one that yields low approximation error on all tasks, the overhead associated with learning such a kernel vanishes and the complexity converges to that of learning when this good kernel is given to the learner.
AU - Pentina, Anastasia
AU - Ben David, Shai
ID - 1706
TI - Multi-task and lifelong learning of kernels
VL - 9355
ER -
TY - JOUR
AB - The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.
AU - Reiter, Johannes
AU - Kanodia, Ayush
AU - Gupta, Raghav
AU - Nowak, Martin
AU - Chatterjee, Krishnendu
ID - 1709
IS - 1812
JF - Proceedings of the Royal Society of London Series B Biological Sciences
TI - Biological auctions with multiple rewards
VL - 282
ER -