Variational studies and replica symmetry breaking in the generalization problem of the binary perceptron

We analyze the average performance of a general class of learning algorithms for the nondeterministic polynomial time complete problem of rule extraction by a binary perceptron. The examples are generated by a rule implemented by a teacher network of similar architecture. A variational approach is used in trying to identify the potential energy that leads to the largest generalization in the thermodynamic limit. We restrict our search to algorithms that always satisfy the binary constraints. A replica symmetric ansatz leads to a learning algorithm which presents a phase transition in violation of an information theoretical bound. Stability analysis shows that this is due to a failure of the replica symmetric ansatz and the first step of replica symmetry breaking (RSB) is studied. The variational method does not determine a unique potential but it allows construction of a class with a unique minimum within each first order valley. Members of this class improve on the performance of Gibbs algorithm but fail to reach the Bayesian limit in the low generalization phase. They even fail to reach the performance of the best binary, an optimal clipping of the barycenter of version space. We find a trade-off between a good low performance and early onset of perfect generalization. Although the RSB may be locally stable we discuss the possibility that it fails to be the correct saddle point globally. ©2000 The American Physical Society.

Variational calculation of positronium-helium-atom scattering length

A basis-set calculation scheme for S-waves Ps-He elastic scattering below the lowest inelastic threshold was formulated using a variational expression for the transition matrix. The scheme was illustrated numerically by calculating the scattering length in the electronic doublet state: a=1.0±0.1 a.u.

Bound constrained smooth optimization for solving variational inequalities and related problems

Variational inequalities and related problems may be solved via smooth bound constrained optimization. A comprehensive discussion of the important features involved with this strategy is presented. Complementarity problems and mathematical programming problems with equilibrium constraints are included in this report. Numerical experiments are commented. Conclusions and directions of future research are indicated.

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: A variational approach

The soliton propagation in a medium with Kerr nonlinearity and resonant impurities was studied by a variational approach. The existence of a solitary wave was shown within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations. The analytical solution which was obtained, was tested through numerical simulations confirming its solitary wave nature.

Variational method for excited states from supersymmetric techniques

We suggest a method for constructing trial eigenfunctions for excited states to be used in the variational method. This method is a generalization of the one that uses a superpotential to obtain the trial functions for the ground state. The construction of an effective hierarchy of Hamiltonians is used to determine excited variational energies. The first four eigenvalues for a quartic double-well potential are calculated for several values of the potential parameter. The results are in very good agreement with the eigenvalues obtained by numerical integration.

Toward an Explanation of the Genesis of Ketamine-Induced Perceptual Distortions and Hallucinatory States

The NMDA receptor (NMDAR) channel has been proposed to function as a coincidence-detection mechanism for afferent and reentrant signals, supporting conscious perception, learning, and memory formation. In this paper we discuss the genesis of distorted perceptual states induced by subanesthetic doses of ketamine, a well-known NMDA antagonist. NMDAR blockage has been suggested to perturb perceptual processing in sensory cortex, and also to decrease GABAergic inhibition in limbic areas (leading to an increase in dopamine excitability). We propose that perceptual distortions and hallucinations induced by ketamine blocking of NMDARs are generated by alternative signaling pathways, which include increase of excitability in frontal areas, and glutamate binding to AMPA in sensory cortex prompting Ca++ entry through voltage-dependent calcium channels (VDCCs). This mechanism supports the thesis that glutamate binding to AMPA and NMDARs at sensory cortex mediates most normal perception, while binding to AMPA and activating VDCCs mediates some types of altered perceptual states. We suggest that Ca++ metabolic activity in neurons at associative and sensory cortices is an important factor in the generation of both kinds of perceptual consciousness.

Confined systems through variational supersymmetric quantum mechanics

The energy states of the confined harmonic oscillator and the Hulthén potentials are evaluated using the Variational Method associated to Supersymmetric Quantum Mechanics.

Smoking is associated with remodeling of gap junction in the rat heart: Smoker's paradox explanation?

Background: In a previous study utilizing the rat model, exposure to tobacco smoke for 5 weeks increased survival after AMI, despite similar age and infarct size between the smokers and nonsmokers, and absence of reperfusion. Objective: Thus, this study aimed to analyze the effects of exposure to tobacco smoke on intensity, distribution or phosphorylation of connexin 43 in the rat heart. Methods: Wistar rats weighing 100 g were randomly allocated into 2 groups: 1) Control (n = 25); 2) Exposed to tobacco smoke (ETS), n = 23. After 5 weeks, left ventricular morphometric analysis, immunohisthochemistry and western blotting for connexin 43 (Cx43) were performed. Results: Collagen volume fraction, cross-sectional areas, and ventricular weight were not statistically different between control and ETS. ETS showed lower stain intensity of Cx43 at intercalated disks (Control: 2.32 ± 0.19; ETS: 1.73 ± 0.18; p = 0.04). The distribution of CX43 at intercalated disks did not differ between the groups (Control: 3.73 ± 0.12; ETS: 3.20 ± 0.17; p = 0.18). ETS rats showed higher levels of dephosphorylated form of Cx43 (Control: 0.45 ± 0.11; ETS: 0.90 ± 0.11; p = 0.03). On the other hand, total Cx43 did not differ between control and ETS groups (Control: 0.75 ± 0.19; ETS: 0.93 ± 0.27; p = 0.58). Conclusion: Exposure to tobacco smoke resulted in cardiac gap junction remodeling, characterized by alterations in the quantity and phosphorylation of the Cx43, in rats hearts. This finding could explain the smoker's paradox observed in some studies.

The psychobiological model: a new explanation to intensity regulation and (in)tolerance in endurance exercise

The mechanisms underpinning fatigue and exhaustion, and the specific sources of exercise-endurance intensity regulation and (in)tolerance have been investigated for over a century. Although several scientific theories are currently available, over the past five years a new framework called Psychobiological model has been proposed. This model gives greater attention to perceptual and motivational factors than its antecedents, and their respective influence on the conscious process of decision-making and behavioral regulation. In this review we present experimental evidences and summarize the key points of the Psychobiological model to explain intensity regulation and (in)tolerance in endurance exercise. Still, we discuss how the Psychobiological model explains training-induced adaptations related to improvements in performance, experimental manipulations, its predictions, and propose future directions for this investigative area. The Psychobiological model may give a new perspective to the results already published in the literature, helping scientists to better guide their research problems, as well as to analyze and interpret new findings more accurately.

Supervised variational relevance learning, an analytic geometric feature selection with applications to omic datasets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Variational and perturbative schemes for a spiked harmonic oscillator

A variational analysis of the spiked harmonic oscillator Hamiltonian operator - d2/dx2 + x2 + l(l + 1)/x2 + λ|x| -α, where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schrödinger equation for the linear harmonic oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large coupling perturbative expansion is carried out and the contributions up to fourth-order to the ground state energy are explicitly evaluated. Numerical results are compared for the special case α = 5/2. © 1989 American Institute of Physics.

Taylor's power law for ecological communities: an explanation on nonextensive/nonlinear statistical grounds

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Identifying regulational alterations in gene regulatory networks by state space representation of vector autoregressive models and variational annealing

Background: In the analysis of effects by cell treatment such as drug dosing, identifying changes on gene network structures between normal and treated cells is a key task. A possible way for identifying the changes is to compare structures of networks estimated from data on normal and treated cells separately. However, this approach usually fails to estimate accurate gene networks due to the limited length of time series data and measurement noise. Thus, approaches that identify changes on regulations by using time series data on both conditions in an efficient manner are demanded. Methods: We propose a new statistical approach that is based on the state space representation of the vector autoregressive model and estimates gene networks on two different conditions in order to identify changes on regulations between the conditions. In the mathematical model of our approach, hidden binary variables are newly introduced to indicate the presence of regulations on each condition. The use of the hidden binary variables enables an efficient data usage; data on both conditions are used for commonly existing regulations, while for condition specific regulations corresponding data are only applied. Also, the similarity of networks on two conditions is automatically considered from the design of the potential function for the hidden binary variables. For the estimation of the hidden binary variables, we derive a new variational annealing method that searches the configuration of the binary variables maximizing the marginal likelihood. Results: For the performance evaluation, we use time series data from two topologically similar synthetic networks, and confirm that our proposed approach estimates commonly existing regulations as well as changes on regulations with higher coverage and precision than other existing approaches in almost all the experimental settings. For a real data application, our proposed approach is applied to time series data from normal Human lung cells and Human lung cells treated by stimulating EGF-receptors and dosing an anticancer drug termed Gefitinib. In the treated lung cells, a cancer cell condition is simulated by the stimulation of EGF-receptors, but the effect would be counteracted due to the selective inhibition of EGF-receptors by Gefitinib. However, gene expression profiles are actually different between the conditions, and the genes related to the identified changes are considered as possible off-targets of Gefitinib. Conclusions: From the synthetically generated time series data, our proposed approach can identify changes on regulations more accurately than existing methods. By applying the proposed approach to the time series data on normal and treated Human lung cells, candidates of off-target genes of Gefitinib are found. According to the published clinical information, one of the genes can be related to a factor of interstitial pneumonia, which is known as a side effect of Gefitinib.

Variational second order flow estimation for PIV sequences

[EN] We present in this paper a variational approach to accurately estimate simultaneously the velocity field and its derivatives directly from PIV image sequences. Our method differs from other techniques that have been presented in the literature in the fact that the energy minimization used to estimate the particles motion depends on a second order Taylor development of the flow. In this way, we are not only able to compute the motion vector field, but we also obtain an accurate estimation of their derivatives. Hence, we avoid the use of numerical schemes to compute the derivatives from the estimated flow that usually yield to numerical amplification of the inherent uncertainty on the estimated flow. The performance of our approach is illustrated with the estimation of the motion vector field and the vorticity on both synthetic and real PIV datasets.

A variational approach to camera motion smoothing

[EN] In this paper we study a variational problem derived from a computer vision application: video camera calibration with smoothing constraint. By video camera calibration we meanto estimate the location, orientation and lens zoom-setting of the camera for each video frame taking into account image visible features. To simplify the problem we assume that the camera is mounted on a tripod, in such case, for each frame captured at time t , the calibration is provided by 3 parameters : (1) P(t) (PAN) which represents the tripod vertical axis rotation, (2) T(t) (TILT) which represents the tripod horizontal axis rotation and (3) Z(t) (CAMERA ZOOM) the camera lens zoom setting. The calibration function t -> u(t) = (P(t),T(t),Z(t)) is obtained as the minima of an energy function I[u] . In thIs paper we study the existence of minima of such energy function as well as the solutions of the associated Euler-Lagrange equations.