Stochastic Variance Reduction Methods for Saddle-Point Problems

We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly convergent algorithms for this class of problems which is common in machine learning. While the algorithmic extension is straightforward, it comes with challenges and opportunities: (a) the convex minimization analysis does not apply and we use the notion of monotone operators to prove convergence, showing in particular that the same algorithm applies to a larger class of problems, such as variational inequalities, (b) there are two notions of splits, in terms of functions, or in terms of partial derivatives, (c) the split does need to be done with convex-concave terms, (d) non-uniform sampling is key to an efficient algorithm, both in theory and practice, and (e) these incremental algorithms can be easily accelerated using a simple extension of the "catalyst" framework, leading to an algorithm which is always superior to accelerated batch algorithms.Comment: Neural Information Processing Systems (NIPS), 2016, Barcelona, Spai

The face inhibition effect: Social contrast or motor competition?

Merely viewing the faces of famous athletes affects the observers' motor system, suggesting that actionbased information is a core feature of person representations, even when no specific action is visible (Bach & Tipper, 2006). Unexpectedly, these person-based motor priming effects were inhibitory. Foot responses were slower when identifying footballers, and hand responses for tennis players. Here, we demonstrate that these inhibitory effects are only evoked when action is implicitly associated with the athletes; when the athletes are seen performing their skilled actions the effect reverses towards facilitation. The contrast between inhibition evoked by implicit action priming and facilitation evoked by the explicit presentation of an action supports the notion of inhibitory control in the motor system. We hypothesise that when no specific action is perceived, a range of actions are activated triggering lateral inhibition, whereas when a specific action is viewed, there is no competition and excitation facilitates similar responses. © 2011 Psychology Press

Can't touch this: the first-person perspective provides privileged access to predictions of sensory action outcomes.

RCUK Open Access funded. ESRC ES/J019178/1Previous studies have shown that viewing others in pain activates cortical somatosensory processing areas and facilitates the detection of tactile targets. It has been suggested that such shared representations have evolved to enable us to better understand the actions and intentions of others. If this is the case, the effects of observing others in pain should be obtained from a range of viewing perspectives. Therefore, the current study examined the behavioral effects of observed grasps of painful and nonpainful objects from both a first- and third-person perspective. In the first-person perspective, a participant was faster to detect a tactile target delivered to their own hand when viewing painful grasping actions, compared with all nonpainful actions. However, this effect was not revealed in the third-person perspective. The combination of action and object information to predict the painful consequences of another person's actions when viewed from the first-person perspective, but not the third-person perspective, argues against a mechanism ostensibly evolved to understand the actions of others

ECONOMIC FEASIBILITY OF USING BRUSH CONTROL TO ENHANCE OFF-SITE WATER YIELD

A feasibility study of brush for off-site water yield was undertaken in 1998 on the North Concho River near San Angelo, Texas. Subsequently, studies were conducted on eight additional Texas watersheds. Economic analysis was based on estimated control costs of the different options compared to the estimated rancher benefits of brush control. Control costs included initial and follow-up treatments required to reduce brush canopy to between 3 and 8%, and maintain it at the reduced level for 10 years. The state cost-share was estimated by subtracting the present value of rancher benefits from the present value of the total cost of the control program. The total cost of additional water was determined by dividing the total state cost-share if all eligible acreage were enrolled by the total added water estimated to result from the brush control program. This procedure resulted in present values of total control costs per acre ranging from $33.75 to$159.45. Rancher benefits, based on the present value of the improved net returns to typical cattle, sheep, goat, and wildlife enterprises, ranged from $8.95 to$52.12 per acre. Present values of the state cost-share per acre ranged from $21.70 to$138.85. The cost of added water estimated for the eight watersheds ranged from $16.41 to$204.05 per acre-foot averaged over each watershed.Resource /Energy Economics and Policy,

Bosonic versus fermionic pairs of topological spin defects in monolayered high-T_c superconductors

The energy associated with bosonic and fermionic pairs of topological spin defects in doped antiferromagnetic quantum spin-1/2 square lattice is estimated within a resonating valence bond scenario, as described by a t-t'-J-like model Hamiltonian, plus a t-perpendicular, responsible of a three-dimensional screening of the electrostatic repulsion within the bosonic pairs. For parameters appropriate for monolayered high-T_c superconductors, both fermionic and bosonic pairs show x^2-y^2 symmetry. We find a critical value of doping such that the energy of the bosonic pairs goes below twice the energy of two fermionic pairs at their Fermi level. This finding could be related to the onset of high-T_c superconductivity.Comment: 10 pages, 6 figures. To be published in Phys. Rev.

Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation

As a contribution to the study of Hartree-Fock theory we prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential mu) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree-Fock theory we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, {S}_z = sum_x n_{x,\uparrow} - n_{x,\downarrow}, and we find that the choice 2{S}_z = N = particle number gives the lowest energy at fixed 0 < mu < 4d.Comment: v2: Published version. 30 pages latex. Changes in title, abstract, introductio

"Feeling" others' painful actions: the sensorimotor integration of pain and action information.

Sensorimotor regions of the brain have been implicated in simulation processes such as action understanding and empathy, but their functional role in these processes remains unspecified. We used functional magnetic resonance imaging (fMRI) to demonstrate that postcentral sensorimotor cortex integrates action and object information to derive the sensory outcomes of observed hand-object interactions. When subjects viewed others' hands grasping or withdrawing from objects that were either painful or nonpainful, distinct sensorimotor subregions emerged as showing preferential responses to different aspects of the stimuli: object information (noxious vs. innocuous), action information (grasps vs. withdrawals), and painful action outcomes (painful grasps vs. all other conditions). Activation in the latter region correlated with subjects' ratings of how painful each object would be to touch and their previous experience with the object. Viewing others' painful grasps also biased behavioral responses to actual tactile stimulation, a novel effect not seen for auditory control stimuli. Somatosensory cortices, including primary somatosensory areas 1/3b and 2 and parietal area PF, may therefore subserve somatomotor simulation processes by integrating action and object information to anticipate the sensory consequences of observed hand-object interactions

Coexistence of Antiferromagnetism and Superconductivity in Electron-doped High-Tc Superconductors

We present magnetotransport evidence for antiferromagnetism in films of the electron-doped cuprates Pr$_{2-x}$Ce$_x$CuO$_4$. Our results show clear signature of static antiferromagnetism up to optimal doping x=0.15, with a quantum phase transition close to x=0.16, and a coexistence of static antiferromagnetism and superconductivity for 0.12$\le$x$\le$0.15