We propose a deep generative model that performs typography analysis and font reconstruction by learning disentangled manifolds of both font style and character shape. Our approach enables us to massively scale up the number of character types we can
effectively model compared to previous methods. Specifically, we infer separate latent variables representing character and font via a pair of inference networks which take as input sets of glyphs that either all share a character type, or belong to the same font. This design allows our model to generalize to characters that were not observed during training time, an important task in light of the relative sparsity of most fonts. We also put forward a new loss, adapted from prior work that measures likelihood using an adaptive distribution in a projected space, resulting in more natural images without requiring a discriminator. We evaluate on the task of font reconstruction over various datasets representing character types of many languages, and compare favorably to modern style transfer systems according to both automatic and manually-evaluated metrics.
We studied the magnetic properties of YCu$_3$(OH)$_6$Br$_2$[Br$_{1-x}$(OH)$_{x}$] ($x$ = 0.33 and 0.45), where Cu$^{2+}$ ions form two-dimensional kagome layers. There is no magnetic order down to 50 mK while the Curie-Weiss temperature is in the ord
er of -100 K. At zero magnetic field, the low-temperature specific heat shows a $T^2$ dependence. Above 2 T, a linear-temperature dependence term in specific heat emerges, and the value of $gamma = C/T$ increases linearly with the field. Furthermore, the magnetic susceptibility tends to a constant value at $T = 0$. Our results suggest that the magnetic ground state of YCu$_3$(OH)$_6$Br$_2$[Br$_{1-x}$(OH)$_{x}$] is consistent with a Dirac quantum-spin-liquid state with linearly dispersing spinon strongly coupled with emergent gauge field, which has long been theoretically proposed as a candidate ground state in the two-dimensional kagome Heisenberg antiferromagnetic system.
We study the magnetic properties of CaFeTi$_2$O$_6$ (CFTO) by high-field magnetization and specific heat measurements. While the magnetic susceptibility data yield a vanishingly small Curie-Weiss temperature, the magnetic moments are not fully polari
zed in magnetic field up to 60 T, which reveals a large spin exchange energy scale. Yet, the system shows no long range magnetic order but a spin-glass-like state below 5.5 K in zero field, indicating strong magnetic frustration in this system. Applying magnetic field gradually suppresses the spin-glass-like state and gives rise to a potential quantum spin liquid state whose low-temperature specific heat exhibits a $T^{1.6}$ power-law. Crucially, conventional mechanisms for frustration do not apply to this system as it possesses neither apparent geometrical frustration nor exchange frustration. We suggest that the orbital modulation of exchange interaction is likely the source of hidden frustration in CFTO, and its full characterization may open a new route in the quest for quantum spin liquids.
Quantum spin liquids (QSLs) are an exotic state of matter that is subject to extensive research. However, the relationship between the ubiquitous disorder and the QSL behaviors is still unclear. Here, by performing comparative experimental studies on
two kagom{e}-lattice QSL candidates, Tm$_3$Sb$_3$Zn$_2$O$_{14}$ and Tm$_3$Sb$_3$Mg$_2$O$_{14}$, which are isostructural to each other but with strong and weak structural disorder, respectively, we show unambiguously that the disorder can induce spin-liquid-like features. In particular, both compounds show dominant antiferromagnetic interactions with a Curie-Weiss temperature of -17.4 and -28.7 K for Tm$_3$Sb$_3$Zn$_2$O$_{14}$ and Tm$_3$Sb$_3$Mg$_2$O$_{14}$, respectively, but remain disordered down to about 0.05 K. Specific heat results suggest the presence of gapless magnetic excitations characterized by a residual linear term. Magnetic excitation spectra obtained by inelastic neutron scattering (INS) at low temperatures display broad continua. All these observations are consistent with those of a QSL. However, we find in Tm$_3$Sb$_3$Zn$_2$O$_{14}$ which has strong disorder resulting from the random mixing of the magnetic Tm$^{3+}$ and nonmagnetic Zn$^{2+}$, that the low-energy magnetic excitations observed in the specific heat and INS measurements are substantially enhanced, compared to those of Tm$_3$Sb$_3$Mg$_2$O$_{14}$ which has much less disorder. We believe that the effective spins of the Tm$^{3+}$ ions in the Zn$^{2+}$/Mg$^{2+}$ sites give rise to the low-energy magnetic excitations, and the amount of the random occupancy determines the excitation strength. These results provide direct evidence of the mimicry of a QSL caused by disorder.
Magnetization measurements and time-of-flight neutron powder-diffraction studies on the high-temperature (300--980 K) magnetism and crystal structure (321--1200 K) of a pulverized YCrO$_3$ single crystal have been performed. Temperature-dependent inv
erse magnetic susceptibility coincides with a piecewise linear function with five regimes, with which we fit a Curie-Weiss law and calculate the frustration factor $f$. The fit results indicate a formation of magnetic polarons between 300 and 540 K and a very strong magnetic frustration. By including one factor $eta$ that represents the degree of spin interactions into the Brillouin function, we can fit well the applied-magnetic-field dependence of magnetization. No structural phase transition was observed from 321 to 1200 K. The average thermal expansions of lattice configurations (emph{a}, emph{b}, emph{c}, and emph{V}) obey well the Gr$ddot{textrm{u}}$neisen approximations with an anomaly appearing around 900 K, implying an isosymmetric structural phase transition, and display an anisotropic character along the crystallographic emph{a}, emph{b}, and emph{c} axes with the incompressibility $K^a_0 > K^c_0 > K^b_0$. It is interesting to find that at 321 K, the local distortion size $Delta$(O2) $approx$ 1.96$Delta$(O1) $approx$ 4.32$Delta$(Y) $approx$ 293.89$Delta$(Cr). Based on the refined Y-O and Cr-O bond lengths, we deduce the local distortion environments and modes of Y, Cr, O1, and O2 ions. Especially, the Y and O2 ions display obvious atomic displacement and charge subduction, which may shed light on the dielectric property of the YCrO$_3$ compound. Additionally, by comparing Kramers Mn$^{3+}$ with non-Kramers Cr$^{3+}$ ions, it is noted that being a Kramers or non-Kramers ion can strongly affect the local distortion size, whereas, it may not be able to change the detailed distortion mode.
We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stab
ility facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.
Recent experimental discoveries have brought a diverse set of broken symmetry states to the center stage of research on cuprate superconductors. Here, we focus on a thematic understanding of the diverse phenomenology by exploring a strong-coupling me
chanism of symmetry breaking driven by frustration of antiferromagnetic order. We achieve this through a variational study of a three-band model of the CuO$_2$ plane with Kondo-type exchange couplings between doped oxygen holes and classical copper spins. Two main findings from this strong-coupling multi-band perspective are 1) that the symmetry hierarchy of spin stripe, charge stripe, intra-unit-cell nematic order and isotropic phases are all accessible microscopically within the model, 2) many symmetry-breaking patterns compete with energy differences within a few meV per Cu atom to produce a rich phase diagram. These results indicate that the diverse phenomenology of broken-symmetry states in hole-doped antiferromagnetic charge-transfer insulators may indeed arise from hole-doped frustration of antiferromagnetism.
We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external
stimuli by its translational displacement in the two-dimensional space. Basis functions of the two-dimensional quantum harmonic oscillator in polar coordinates are introduced to describe the distortion modes of the Gaussian bump. The perturbative method is applied to analyze its dynamics. Testing the method by considering the network behavior when the external stimulus abruptly changes its position, we obtain results of the reaction time and the amplitudes of various distortion modes, with excellent agreement with simulation results.
Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to elucidate bra
in functions. This study investigates the tracking dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of neuronal recurrent interactions, CANNs can hold a continuous family of stationary states. They form a continuous manifold in which the neural system is neutrally stable. We systematically explore how this property facilitates the tracking performance of a CANN, which is believed to have clear correspondence with brain functions. By using the wave functions of the quantum harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is decomposed into different motion modes, corresponding to distortions in the amplitude, position, width or skewness of the network state. We then develop a perturbative approach that utilizes the dominating movement of the networks stationary states in the state space. This method allows us to approximate the network dynamics up to an arbitrary accuracy depending on the order of perturbation used. We quantify the distortions of a Gaussian bump during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable and the reaction time for the network to catch up with an abrupt change in the stimulus.
