Many questions of fundamental interest in today's science can be formulated as inference problems: some partial, or noisy, observations are performed over a set of variables and the goal is to ...recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problems, the central scientific questions are: Under what conditions is the information contained in the measurements sufficient for a satisfactory inference to be possible? What are the most efficient algorithms for this task? A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics. Moreover, it turned out that we can use the gained physical insight to develop new promising algorithms. The connection between inference and statistical physics is currently witnessing an impressive renaissance and we review here the current state-of-the-art, with a pedagogical focus on the Ising model which, formulated as an inference problem, we call the planted spin glass. In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear measurements, with compressed sensing as a case of sparse estimation. Our goal is to provide a pedagogical review for researchers in physics and other fields interested in this fascinating topic.
Abstract A self-contained new constructive solution of the mean-field Sherrington-Kirkpatric spin-glass model is obtained from the study of the behaviour of the entropy of the Gibbs measure at low ...temperatures.
We consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics tools, and ...numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram which summarizes their performance as a function of the control parameters (e.g., quality and quantity of the training dataset, network storage, noise), that is valid in the limit of large network-size and structureless datasets. We also numerically test the learning, storing and retrieval capabilities of these networks on structured datasets such as MNist and Fashion MNist. As technical remarks, on the analytic side, we extend Guerra’s interpolation to tackle the non-Gaussian distributions involved in the post-synaptic potentials while, on the computational side, we insert Plefka’s approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate supervised learning in neural networks, beyond the shallow limit.
•The range of solid solutions of Ti-doped Ba-hexaferrites was expanded to 2.00.•Ti-doped Ba-hexaferrites BaFe12−xTixO19 magnetic state interpretation was given.•Mechanism of occupation nonequivalent ...crystallographic positions by Ti was determined.•The spin-glass component of the magnetic phase state is fixed.•The critical magnetic field of the spin-glass component disappearance was found.
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A number of solid solutions based on BaFe12−xTixO19 M-type barium hexaferrite doped with titanium cations up to x = 2.00 were obtained using conventional ceramic technology. The phase composition, crystal structure and unit cell parameters were refined by the Rietveld method using powder X-ray diffraction data up to T = 900 K. It was found that all the compositions have a magnetoplumbite structure satisfactorily described by P63/mmc space group (No. 194). With increasing temperature and doping concentration, the unit cell parameters increase almost monotonically. The minimum volume of V ~ 696.72 Å3 was determined for the composition with x = 1.00 at T = 100 K, while the maximum value of V ~ 714.00 Å3 is observed for the composition with x = 2.00 at T = 900 K. The mechanism of occupation nonequivalent crystallographic positions with titanium cations is established. The spin-glass component of the magnetic phase state is fixed. The Tdif temperature of the difference between the ZFC-FC curves decreases with an increase in the concentration of titanium cations and the magnetic field from ~237.2 K to ~ 44.5 K, while the Tinf inflection temperature of the ZFC curve increases from ~21.0 K to ~23.8 K. With an increase in the doping concentration, both the Dav average and Dmax maximum clusters grow up to ~ 100 nm. As the magnetic field increases above the critical value, the spin-glass component disappears. For compositions with x > 1.00, the magnetization is not saturated in fields up to 6 T. Along with the formation of the spin-glass component, doping with titanium cations for barium hexaferrite lowers the TC Curie temperature down to T ~600 K. The Ms spontaneous and Mr remanent magnetizations, as well as the Bc coercivity, decrease with increasing doping concentration almost monotonically, while the latter has an inflection point at x = 1.00. The minimum values of spontaneous and remanent magnetization, as well as coercivity, are observed for the composition with x = 2.00 and amount to Ms ~17.7 emu/g, Mr ~1.9 emu/g, and Bc ~3.9 × 10−3 T, respectively. An interpretation of the magnetic state of the doped BaFe12−xTixO19 barium hexaferrite is given taking into account the mechanism of occupation nonequivalent crystallographic positions with titanium cations.
We observe the joint spin-spatial (spinor) self-organization of a two-component Bose-Einstein condensate (BEC) strongly coupled to an optical cavity. This unusual nonequilibrium Hepp-Lieb-Dicke phase ...transition is driven by an off-resonant Raman transition formed from a classical pump field and the emergent quantum dynamical cavity field. This mediates a spinor-spinor interaction that, above a critical strength, simultaneously organizes opposite spinor states of the BEC on opposite checkerboard configurations of an emergent 2D lattice. The resulting spinor density-wave polariton condensate is observed by directly detecting the atomic spin and momentum state and by holographically reconstructing the phase of the emitted cavity field. The latter provides a direct measure of the spin state, and a spin-spatial domain wall is observed. The photon-mediated spin interactions demonstrated here may be engineered to create dynamical gauge fields and quantum spin glasses.
We present several efficient implementations of the simulated annealing algorithm for Ising spin glasses on sparse graphs. In particular, we provide a generic code for any choice of couplings, an ...optimised code for bipartite graphs, and highly optimised implementations using multi-spin coding for graphs with small maximum degree and discrete couplings with a finite range. The latter codes achieve up to 50 spin flips per nanosecond on modern Intel CPUs. We also compare the performance of the codes to that of the special purpose D-Wave devices built for solving such Ising spin glass problems.
Program title: SimAn v1.0
Catalogue identifier: AEVZ_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVZ_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: GNU General Public License, version 3
No. of lines in distributed program, including test data, etc.: 14999
No. of bytes in distributed program, including test data, etc.: 26594
Distribution format: tar.gz
Programming language: C++, OpenMP for parallelization.
Computer: Any PC.
Operating system: Linux/OS X/UNIX.
Has the code been vectorised or parallelized?: Parallelized using OpenMP.
RAM: Variable, from a few megabytes.
Classification: 4.13, 6.5, 23.
Nature of problem: Ising spin glass ground states on sparse graphs.
Solution method: Simulated annealing.
Running time: From milliseconds to seconds.
We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix. When the spike comes from a prior that is i.i.d. across coordinates, we ...prove that the log-likelihood ratio of the spiked model against the nonspiked one is asymptotically normal below a certain reconstruction threshold which is not necessarily of a “spectral” nature, and that it is degenerate above. This establishes the maximal region of contiguity between the planted and null models. It is known that this threshold also marks a phase transition for estimating the spike: the latter task is possible above the threshold and impossible below. Therefore, both estimation and detection undergo the same transition in this random matrix model. Further information on the performance of the optimal test is also provided. Our proofs are based on Gaussian interpolation methods and a rigorous incarnation of the cavity method, as devised by Guerra and Talagrand in their study of the Sherrington–Kirkpatrick spin-glass model.
Motivated by the recent discovery of superconductivity in infinite-layer nickelate thin films, we report on a synthesis and magnetization study on bulk samples of the parent compounds RNiO2 (R = La, ...Pr, Nd). The frequency-dependent peaks of the alternating current magnetic susceptibility, along with remarkable memory effects, characterize spin-glass states. Furthermore, various phenomenological parameters via different spin glass models show strong similarity within these three compounds as well as with other rare-earth metal nickelates. The universal spin-glass behaviour distinguishes the nickelates from the parent compound CaCuO2 of cuprate superconductors, which has the same crystal structure and d9 electronic configuration but undergoes a long-range antiferromagnetic order. Our investigations may indicate a distinctly different nature of magnetism and superconductivity in the bulk nickelates than in the cuprates.
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