Effects of spin fluctuations in the t-J model

Recent experiments on the Fermi surface and the electronic structure of the cuprate-supercondutors showed the importance of short range antiferromagnetic correlations for the physics in these systems. Theoretically, features like shadow bands were predicted and calculated mainly for the Hubbard model. In our approach we calculate an approximate selfenergy of the $t$-$J$ model. Solving the $U=\infty$ Hubbard model in the Dynamical Mean Field Theory (DMFT) yields a selfenergy that contains most of the local correlations as a starting point. Effects of the nearest neighbor spin interaction $J$ are then included in a heuristical manner. Formally like in $J$-perturbation theory all ring diagrams, with the single bubble assumed to be purely local, are summed to get a correction to the DMFT-self engergy This procedure causes new bands and can furnish strong deformation of quasiparticle bands. % Our results are finally compared with %former approaches to the Hubbard model.Comment: 3 Pages, Latex, 2 Postscript-Figures submitted to Physica

Spectral Properties and Bandstructure of Correlated Electron Systems

We present $\vec{k}$-dependent one-particle spectra and corresponding effective bandstructures for the $2d$ Hubbard model calculated within the dynamical molecular field theory (DMFT). This method has proven to yield highly nontrivial results for a variety of quantities but the question remains open to what extent it is applicable to relevant physical situations. To address this problem we compare our results for spectral functions to those obtained by QMC simulations. The good agreement supports our notion that the DMFT is indeed a sensible ansatz for correlated models even in to $d=2$.Comment: Paper presented at SCES '95, Sept. 27 - 30 1995, Goa. To be published in Physica B. 10 pages, figures include

Procedural content generation: better benchmarks for transfer reinforcement learning

The idea of transfer in reinforcement learning (TRL) is intriguing: being able to transfer knowledge from one problem to another problem without learning everything from scratch. This promises quicker learning and learning more complex methods. To gain an insight into the field and to detect emerging trends, we performed a database search. We note a surprisingly late adoption of deep learning that starts in 2018. The introduction of deep learning has not yet solved the greatest challenge of TRL: generalization. Transfer between different domains works well when domains have strong similarities (e.g. MountainCar to Cartpole), and most TRL publications focus on different tasks within the same domain that have few differences. Most TRL applications we encountered compare their improvements against self-defined baselines, and the field is still missing unified benchmarks. We consider this to be a disappointing situation. For the future, we note that: (1) A clear measure of task similarity is needed. (2) Generalization needs to improve. Promising approaches merge deep learning with planning via MCTS or introduce memory through LSTMs. (3) The lack of benchmarking tools will be remedied to enable meaningful comparison and measure progress. Already Alchemy and Meta-World are emerging as interesting benchmark suites. We note that another development, the increase in procedural content generation (PCG), can improve both benchmarking and generalization in TRL.LIACS-Managemen

A new challenge: approaching Tetris Link with AI

Decades of research have been invested in making computer programs for playing games such as Chess and Go. This paper introduces a board game, Tetris Link, that is yet unexplored and appears to be highly challenging. Tetris Link has a large branching factor and lines of play that can be very deceptive, that search has a hard time uncovering. Finding good moves is very difficult for a computer player, our experiments show. We explore heuristic planning and two other approaches: Reinforcement Learning and Monte Carlo tree search. Curiously, a naive heuristic approach that is fueled by expert knowledge is still stronger than the planning and learning approaches. We, therefore, presume that Tetris Link is more difficult than expected. We offer our findings to the community as a challenge to improve upon.LIACS-Managemen

Variationnal study of ferromagnetism in the t1-t2 Hubbard chain

A one-dimensional Hubbard model with nearest and (negative) next-nearest neighbour hopping is studied variationally. This allows to exclude saturated ferromagnetism for $U < U_c$. The variational boundary $U_c (n)$ has a minimum at a ``critical density'' $n_c$ and diverges for $n \rightarrow 1$.Comment: 5 pages, LateX and 1 postscript figure. To appear in Physica

Believable Minecraft Settlements by Means of Decentralised Iterative Planning

Procedural city generation that focuses on believability and adaptability to random terrain is a difficult challenge in the field of Procedural Content Generation (PCG). Dozens of researchers compete for a realistic approach in challenges such as the Generative Settlement Design in Minecraft (GDMC), in which our method has won the 2022 competition. This was achieved through a decentralised, iterative planning process that is transferable to similar generation processes that aims to produce "organic" content procedurally.Comment: 8 pages, 8 figures, to be published in "2023 IEEE Conference on Games (CoG)

Shadow band in the one-dimensional large UU Hubbard model

We show that the factorized wave-function of Ogata and Shiba can be used to calculate the $k$ dependent spectral functions of the one-dimensional, infinite $U$ Hubbard model, and of some extensions to finite $U$. The resulting spectral function is remarkably rich: In addition to low energy features typical of Luttinger liquids, there is a well defined band, which we identify as the shadow band resulting from $2k_F$ spin fluctuations. This band should be detectable experimentally because its intensity is comparable to that of the main band for a large range of momenta.Comment: Latex file. 4 pages. Figures upon reques

Diffusion-weighted MRI reflects proliferative activity in primary CNS lymphoma

Purpose: To investigate if apparent diffusion coefficient (ADC) values within primary central nervous system lymphoma correlate with cellularity and proliferative activity in corresponding histological samples. Materials and Methods: Echo-planar diffusion-weighted magnetic resonance images obtained from 21 patients with primary central nervous system lymphoma were reviewed retrospectively. Regions of interest were drawn on ADC maps corresponding to the contrast enhancing parts of the tumors. Biopsies from all 21 patients were histologically analyzed. Nuclei count, total nuclei area and average nuclei area were measured. The proliferation index was estimated as Ki-67 positive nuclei divided by total number of nuclei. Correlations of ADC values and histopathologic parameters were determined statistically. Results: Ki-67 staining revealed a statistically significant correlation with ADCmin (r = -0.454, p = 0.038), ADCmean (r = -0.546, p = 0.010) and ADCmax (r = -0.515, p = 0.017). Furthermore, ADCmean correlated in a statistically significant manner with total nucleic area (r = -0.500, p = 0.021). Conclusion: Low ADCmin, ADCmean and ADCmax values reflect a high proliferative activity of primary cental nervous system lymphoma. Low ADCmean values—in concordance with several previously published studies—indicate an increased cellularity within the tumor