Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finite-many hierarchies are unstable and only the scheme with infinite-many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing the number of hierarchies.Comment: REVTeX4, 11 pages, no figure

Unusual signatures of the ferromagnetic transition in the heavy Fermion compound UMn2_2Al20_{20}

Magnetic susceptibility results for single crystals of the new cubic compounds UT$_2$Al$_{20}$ (T=Mn, V, and Mo) are reported. Magnetization, specific heat, resistivity, and neutron diffraction results for a single crystal and neutron diffraction and inelastic spectra for a powder sample are reported for UMn$_2$Al$_{20}$. For T = V and Mo, temperature independent Pauli paramagnetism is observed. For UMn$_2$Al$_{20}$, a ferromagnetic transition is observed in the magnetic susceptibility at $T_c$ = 20 K. The specific heat anomaly at $T_c$ is very weak while no anomaly in the resistivity is seen at $T_c$. We discuss two possible origins for this behavior of UMn$_2$Al$_{20}$: moderately small moment itinerant ferromagnetism, or induced local moment ferromagnetism.Comment: 5 pages, 5 figures, to be published in Phys. rev.

Parisi Phase in a Neuron

Pattern storage by a single neuron is revisited. Generalizing Parisi's framework for spin glasses we obtain a variational free energy functional for the neuron. The solution is demonstrated at high temperature and large relative number of examples, where several phases are identified by thermodynamical stability analysis, two of them exhibiting spontaneous full replica symmetry breaking. We give analytically the curved segments of the order parameter function and in representative cases compute the free energy, the storage error, and the entropy.Comment: 4 pages in prl twocolumn format + 3 Postscript figures. Submitted to Physical Review Letter

Optimally adapted multi-state neural networks trained with noise

The principle of adaptation in a noisy retrieval environment is extended here to a diluted attractor neural network of Q-state neurons trained with noisy data. The network is adapted to an appropriate noisy training overlap and training activity which are determined self-consistently by the optimized retrieval attractor overlap and activity. The optimized storage capacity and the corresponding retriever overlap are considerably enhanced by an adequate threshold in the states. Explicit results for improved optimal performance and new retriever phase diagrams are obtained for Q=3 and Q=4, with coexisting phases over a wide range of thresholds. Most of the interesting results are stable to replica-symmetry-breaking fluctuations.Comment: 22 pages, 5 figures, accepted for publication in PR

Daytime lidar measurements of tidal winds in the mesospheric sodium layer at Urbana, Illinois

For more than 15 years lidar systems have been used to study the chemistry and dynamics of the mesospheric sodium layer. Because the layer is an excellent tracer of atmospheric wave motions, sodium lidar has proven to be particularly useful for studying the influence of gravity waves and tides on mesospheric dynamics. These waves, which originate in the troposphere and stratosphere, propagate through the mesosphere and dissipate their energy near the mesopause making important contributions to the momentum and turbulence budget in this region of the atmosphere. Recently, the sodium lidar was modified for daytime operation so that wave phenomena and chemical effects could be monitored throughout the complete diurnal cycle. The results of continuous 24 hour lidar observations of the sodium layer structure are presented alond with measurement of the semidiurnal tidal winds

An Electronically Reconfigurable Patch Antenna Design for Polarization Diversity with Fixed Resonant Frequency

In this paper, an electronically polarization reconfigurable circular patch antenna with fixed resonant frequency operating at Wireless Local Area Network (WLAN) frequency band (2.4-2.48 GHz) is presented. The structure of the proposed design consists of a circular patch as a radiating element fed by coaxial probe, cooperated with four equal-length slits etched on the edge along x-axis and y-axis. A total of four switches was used and embedded across the slits at specific locations, thus controlled the length of the slits. By activating and deactivating the switches (ON and OFF) across the slits, the current on the patch is changed, thus modifying the electric field and polarization of the antenna. Consequently, the polarization excited by the proposed antenna can be switched into three types, either linear polarization, left-hand circular polarization or right-hand circular polarization. This paper proposes a simple approach that able to switch the polarizations and excited at the same operating frequency. Simulated and measured results of ideal case (using copper strip switches) and real case (using PIN diode switches) are compared and presented to demonstrate the performance of the antenna

Has education lost sight of children?

The reflections presented in this chapter are informed by clinical and personal experiences of school education in the UK. There are many challenges for children and young people in the modern education system and for the professionals who support them. In the UK, there are significant gaps between the highly selective education provided to those who pay privately for it and to the majority of those educated in the state-funded system. Though literacy rates have improved around the world, many children, particularly boys, do not finish their education for reasons such as boredom, behavioural difficulties or because education does not ‘pay’. Violence, bullying, and sexual harassment are issues faced by many children in schools and there are disturbing trends of excluding children who present with behavioural problems at school whose origins are not explored. Excluded children are then educated with other children who may also have multiple problems which often just make the situation worse. The experience of clinicians suggests that school-related mental health problems are increasing in severity. Are mental health services dealing with the consequences of an education system that is not meeting children’s needs? An education system that is testing- and performance-based may not be serving many children well if it is driving important decisions about them at increasingly younger ages. Labelling of children and setting them on educational career paths can occur well before they reach secondary schools, limiting potential very early on in their developmental trajectory. Furthermore, the emphasis at school on testing may come at the expense of creativity and other forms of intelligence, which are also valuable and important. Meanwhile the employment marketplace requires people with widely different skills, with an emphasis on innovation, creativity, and problem solving. Is education losing sight of the children it is educating

A Two-Player Game of Life

We present a new extension of Conway's game of life for two players, which we call p2life. P2life allows one of two types of token, black or white, to inhabit a cell, and adds competitive elements into the birth and survival rules of the original game. We solve the mean-field equation for p2life and determine by simulation that the asymptotic density of p2life approaches 0.0362.Comment: 7 pages, 3 figure

Application of two-parameter dynamical replica theory to retrieval dynamics of associative memory with non-monotonic neurons

The two-parameter dynamical replica theory (2-DRT) is applied to investigate retrieval properties of non-monotonic associative memory, a model which lacks thermodynamic potential functions. 2-DRT reproduces dynamical properties of the model quite well, including the capacity and basin of attraction. Superretrieval state is also discussed in the framework of 2-DRT. The local stability condition of the superretrieval state is given, which provides a better estimate of the region in which superretrieval is observed experimentally than the self-consistent signal-to-noise analysis (SCSNA) does.Comment: 16 pages, 19 postscript figure

Dimensional Evolution of Spin Correlations in the Magnetic Pyrochlore Yb2Ti2O7

The pyrochlore material Yb2Ti2O7 displays unexpected quasi-two-dimensional (2D) magnetic correlations within a cubic lattice environment at low temperatures, before entering an exotic disordered ground state below T=265mK. We report neutron scattering measurements of the thermal evolution of the 2D spin correlations in space and time. Short range three dimensional (3D) spin correlations develop below 400 mK, accompanied by a suppression in the quasi-elastic (QE) scattering below ~ 0.2 meV. These show a slowly fluctuating ground state with spins correlated over short distances within a kagome-triangular-kagome (KTK) stack along [111], which evolves to isolated kagome spin-stars at higher temperatures. Furthermore, low-temperature specific heat results indicate a sample dependence to the putative transition temperature that is bounded by 265mK, which we discuss in the context of recent mean field theoretical analysis.Comment: 5 pages, 6 figure