Model simulation studies to clarify the effect on saccadic eye movements of initial condition velocities set by the Vestibular Ocular Reflex (VOR)

Voluntary active head rotations produced vestibulo-ocular reflex eye movements (VOR) with the subject viewing a fixation target. When this target jumped, the size of the refixation saccades were a function of the ongoing initial velocity of the eye. Saccades made against the VOR were larger in magnitude. Simulation of a reciprocally innervated model eye movement provided results comparable to the experimental data. Most of the experimental effect appeared to be due to linear summation for saccades of 5 and 10 degree magnitude. For small saccades of 2.5 degrees, peripheral nonlinear interaction of state variables in the neuromuscular plant also played a role as proven by comparable behavior in the simulated model with known controller signals

Short range ferromagnetism and spin glass state in Y0.7Ca0.3MnO3\mathrm{Y_{0.7}Ca_{0.3}MnO_{3}}

Dynamic magnetic properties of $\mathrm{Y_{0.7}Ca_{0.3}MnO_{3}}$ are reported. The system appears to attain local ferromagnetic order at $T_{\mathrm{SRF}} \approx 70$ K. Below this temperature the low field magnetization becomes history dependent, i.e. the zero field cooled (ZFC) and field cooled (FC) magnetization deviate from each other and closely logarithmic relaxation appears at our experimental time scales (0.3-$10^{4}$ sec). The zero field cooled magnetization has a maximum at $T_{\mathrm{f}}\approx 30$ K, whereas the field cooled magnetization continues to increase, although less sharply, also below this temperature. Surprisingly, the dynamics of the system shows non-equilibrium spin glass (SG) features not only below the maximum in the ZFC magnetization, but also in the temperature region between this maximum and $T_{\mathrm{SRF}}$. The aging and temperature cycling experiments show only quantitative differences in the dynamic behavior above and below the maximum in the ZFC-magnetization; similarly, memory effects are observed in both temperature regions. We attribute the high temperature behavior to the existence of clusters of short range ferromagnetic order below $T_{\mathrm{SRF}}$; the configuration evolves into a conventional spin glass state at temperatures below $T_{\mathrm{f}}$.Comment: REVTeX style; 8 pages, 8 figure

Inverse velocity statistics in two dimensional turbulence

We present a numerical study of two-dimensional turbulent flows in the enstrophy cascade regime, with different large-scale forcings and energy sinks. In particular, we study the statistics of more-than-differentiable velocity fluctuations by means of two recently introduced sets of statistical estimators, namely {\it inverse statistics} and {\it second order differences}. We show that the 2D turbulent velocity field, $\bm u$, cannot be simply characterized by its spectrum behavior, $E(k) \propto k^{-\alpha}$. There exists a whole set of exponents associated to the non-trivial smooth fluctuations of the velocity field at all scales. We also present a numerical investigation of the temporal properties of $\bm u$ measured in different spatial locations.Comment: 9 pages, 12 figure

Memory and superposition in a spin glass

Non-equilibrium dynamics in a Ag(Mn) spin glass are investigated by measurements of the temperature dependence of the remanent magnetisation. Using specific cooling protocols before recording the thermo- or isothermal remanent magnetisations on re-heating, it is found that the measured curves effectively disclose non-equilibrium spin glass characteristics such as ageing and memory phenomena as well as an extended validity of the superposition principle for the relaxation. The usefulness of this "simple" dc-method is discussed, as well as its applicability to other disordered magnetic systems.Comment: REVTeX style; 8 pages, 4 figure

Area spectra of the rotating BTZ black hole from quasinormal modes

Following Bekenstein's suggestion that the horizon area of a black hole should be quantized, the discrete spectrum of the horizon area has been investigated in various ways. By considering the quasinormal mode of a black hole, we obtain the transition frequency of the black hole, analogous to the case of a hydrogen atom, in the semiclassical limit. According to Bohr's correspondence principle, this transition frequency at large quantum number is equal to classical oscillation frequency. For the corresponding classical system of periodic motion with this oscillation frequency, an action variable is identified and quantized via Bohr-Sommerfeld quantization, from which the quantized spectrum of the horizon area is obtained. This method can be applied for black holes with discrete quasinormal modes. As an example, we apply the method for the both non-rotating and rotating BTZ black holes and obtain that the spectrum of the horizon area is equally spaced and independent of the cosmological constant for both cases

Out-of-Distribution Generalization in Algorithmic Reasoning Through Curriculum Learning

Out-of-distribution generalization (OODG) is a longstanding challenge for neural networks, and is quite apparent in tasks with well-defined variables and rules, where explicit use of the rules can solve problems independently of the particular values of the variables. Large transformer-based language models have pushed the boundaries on how well neural networks can generalize to novel inputs, but their complexity obfuscates they achieve such robustness. As a step toward understanding how transformer-based systems generalize, we explore the question of OODG in smaller scale transformers. Using a reasoning task based on the puzzle Sudoku, we show that OODG can occur on complex problems if the training set includes examples sampled from the whole distribution of simpler component tasks