Comparison of non-crossing perturbative approach and generalized projection method for strongly coupled spin-fermion systems at low doping

We analyze the two-dimensional spin-fermion model in the strong coupling regime relevant to underdoped cuprates. We recall the set of general sumrules that relate moments of spectral density and the imaginary part of fermion self-energy with static correlation functions. We show that two-pole approximation of projection method satisfies the sumrules for first four moments of spectral density and gives an exact upper bound for quasiparticle energy near the band bottom. We prove that non-crossing approximation that is often made in perturbative consideration of the model violates the sumrule for third moment of spectral density. This leads to wrong position of lowest quasiparticle band. On the other hand, the projection method is inadequate in weak coupling limit because of approximate treatment of kinetic energy term. We propose a generalization of projection method that overcomes this default and give the fermion self-energy that correctly behaves both in weak and strong coupling limits.Comment: 9 pages, 4 EPS figures, RevTe

Perfect and near perfect adaptation in a model of bacterial chemotaxis

The signaling apparatus mediating bacterial chemotaxis can adapt to a wide range of persistent external stimuli. In many cases, the bacterial activity returns to its pre-stimulus level exactly and this "perfect adaptability" is robust against variations in various chemotaxis protein concentrations. We model the bacterial chemotaxis signaling pathway, from ligand binding to CheY phosphorylation. By solving the steady-state equations of the model analytically, we derive a full set of conditions for the system to achieve perfect adaptation. The conditions related to the phosphorylation part of the pathway are discovered for the first time, while other conditions are generalization of the ones found in previous works. Sensitivity of the perfect adaptation is evaluated by perturbing these conditions. We find that, even in the absence of some of the perfect adaptation conditions, adaptation can be achieved with near perfect precision as a result of the separation of scales in both chemotaxis protein concentrations and reaction rates, or specific properties of the receptor distribution in different methylation states. Since near perfect adaptation can be found in much larger regions of the parameter space than that defined by the perfect adaptation conditions, their existence is essential to understand robustness in bacterial chemotaxis.Comment: 16 pages, 9 figure

Exact Dynamics of the SU(K) Haldane-Shastry Model

The dynamical structure factor $S(q,\omega)$ of the SU(K) (K=2,3,4) Haldane-Shastry model is derived exactly at zero temperature for arbitrary size of the system. The result is interpreted in terms of free quasi-particles which are generalization of spinons in the SU(2) case; the excited states relevant to $S(q,\omega)$ consist of K quasi-particles each of which is characterized by a set of K-1 quantum numbers. Near the boundaries of the region where $S(q,\omega)$ is nonzero, $S(q,\omega)$ shows the power-law singularity. It is found that the divergent singularity occurs only in the lowest edges starting from $(q,\omega) = (0,0)$ toward positive and negative q. The analytic result is checked numerically for finite systems via exact diagonalization and recursion methods.Comment: 35 pages, 3 figures, youngtab.sty (version 1.1

Online Influence Maximization under Independent Cascade Model with Semi-Bandit Feedback

We study the online influence maximization problem in social networks under the independent cascade model. Specifically, we aim to learn the set of "best influencers" in a social network online while repeatedly interacting with it. We address the challenges of (i) combinatorial action space, since the number of feasible influencer sets grows exponentially with the maximum number of influencers, and (ii) limited feedback, since only the influenced portion of the network is observed. Under a stochastic semi-bandit feedback, we propose and analyze IMLinUCB, a computationally efficient UCB-based algorithm. Our bounds on the cumulative regret are polynomial in all quantities of interest, achieve near-optimal dependence on the number of interactions and reflect the topology of the network and the activation probabilities of its edges, thereby giving insights on the problem complexity. To the best of our knowledge, these are the first such results. Our experiments show that in several representative graph topologies, the regret of IMLinUCB scales as suggested by our upper bounds. IMLinUCB permits linear generalization and thus is both statistically and computationally suitable for large-scale problems. Our experiments also show that IMLinUCB with linear generalization can lead to low regret in real-world online influence maximization.Comment: Compared with the previous version, this version has fixed a mistake. This version is also consistent with the NIPS camera-ready versio

Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries

Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model in which the goal is to compute functions of N by N ``black box'' unitary matrices drawn from a set of such matrices, a problem with applications to determining properties of quantum physical systems. We characterize the existence of an algorithm for such a query problem, with given error and number of queries, as equivalent to the feasibility of a certain set of semidefinite programming constraints, or equivalently the infeasibility of a dual of these constraints, which we construct. Relaxing the primal constraints to correspond to mere pairwise near-orthogonality of the final states of a quantum computer, conditional on black-box inputs having distinct function values, rather than bounded-error determinability of the function value via a single measurement on the output states, we obtain a relaxed primal program the feasibility of whose dual still implies the nonexistence of a quantum algorithm. We use this to obtain a generalization, to our not-necessarily-commutative setting, of the ``spectral adversary method'' for quantum query lower bounds.Comment: Dagstuhl Seminar Proceedings 06391, "Algorithms and Complexity for Continuous Problems," ed. S. Dahlke, K. Ritter, I. H. Sloan, J. F. Traub (2006), available electronically at http://drops.dagstuhl.de/portals/index.php?semnr=0639

On the spectra of scalar mesons from HQCD models

We determine the holographic spectra of scalar mesons from the fluctuations of the embedding of flavor D-brane probes in HQCD models. The models we consider include a generalization of the Sakai Sugimoto model at zero temperature and at the "high-temperature intermediate phase", where the system is in a deconfining phase while admitting chiral symmetry breaking and a non-critical 6d model at zero temperature. All these models are based on backgrounds associated with near extremal N_c D4 branes and a set of N_f<<N_c flavor probe branes that admit geometrical chiral symmetry breaking. We point out that the spectra of these models include a 0^{--} branch which does not show up in nature. At zero temperature we found that the masses of the mesons M_n depend on the "constituent quark mass" parameter m^c_q and on the excitation number n as M_n^2 m^c_q and M^2_n n^{1.7} for the ten dimensional case and as M_n m^c_q and M_n n^{0.75} in the non-critical case. At the high temperature intermediate phase we detect a decrease of the masses of low spin mesons as a function of the temperature similar to holographic vector mesons and to lattice calculations.Comment: 22 pages, 12 figure

Relating Regularization and Generalization through the Intrinsic Dimension of Activations

Given a pair of models with similar training set performance, it is natural to assume that the model that possesses simpler internal representations would exhibit better generalization. In this work, we provide empirical evidence for this intuition through an analysis of the intrinsic dimension (ID) of model activations, which can be thought of as the minimal number of factors of variation in the model's representation of the data. First, we show that common regularization techniques uniformly decrease the last-layer ID (LLID) of validation set activations for image classification models and show how this strongly affects generalization performance. We also investigate how excessive regularization decreases a model's ability to extract features from data in earlier layers, leading to a negative effect on validation accuracy even while LLID continues to decrease and training accuracy remains near-perfect. Finally, we examine the LLID over the course of training of models that exhibit grokking. We observe that well after training accuracy saturates, when models ``grok'' and validation accuracy suddenly improves from random to perfect, there is a co-occurent sudden drop in LLID, thus providing more insight into the dynamics of sudden generalization.Comment: NeurIPS 2022 OPT and HITY workshop