Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks

Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees about their behavior. We present a novel, scalable, and efficient technique for verifying properties of deep neural networks (or providing counter-examples). The technique is based on the simplex method, extended to handle the non-convex Rectified Linear Unit (ReLU) activation function, which is a crucial ingredient in many modern neural networks. The verification procedure tackles neural networks as a whole, without making any simplifying assumptions. We evaluated our technique on a prototype deep neural network implementation of the next-generation airborne collision avoidance system for unmanned aircraft (ACAS Xu). Results show that our technique can successfully prove properties of networks that are an order of magnitude larger than the largest networks verified using existing methods.Comment: This is the extended version of a paper with the same title that appeared at CAV 201

Application of semidefinite programming to maximize the spectral gap produced by node removal

The smallest positive eigenvalue of the Laplacian of a network is called the spectral gap and characterizes various dynamics on networks. We propose mathematical programming methods to maximize the spectral gap of a given network by removing a fixed number of nodes. We formulate relaxed versions of the original problem using semidefinite programming and apply them to example networks.Comment: 1 figure. Short paper presented in CompleNet, Berlin, March 13-15 (2013

Unbiased Global Optimization of Lennard-Jones Clusters for N <= 201 by Conformational Space Annealing Method

We apply the conformational space annealing (CSA) method to the Lennard-Jones clusters and find all known lowest energy configurations up to 201 atoms, without using extra information of the problem such as the structures of the known global energy minima. In addition, the robustness of the algorithm with respect to the randomness of initial conditions of the problem is demonstrated by ten successful independent runs up to 183 atoms. Our results indicate that the CSA method is a general and yet efficient global optimization algorithm applicable to many systems.Comment: revtex, 4 pages, 2 figures. Physical Review Letters, in pres

Saccadic eye velocity after selective GABAergic treatment with tiagabine in healthy volunteers

Background: Saccadic eye velocity (SEV) has been shown to be a reliable neurophysiological tool for the assessment of gamma-aminobutyric acid GABA(A) receptor sensitivity. Administration of benzodiazepines targeting the GABA(A) receptor decreases SEV in healthy volunteers. Tiagabine is a new antiepileptic drug which acts via selective blockade of GABA reuptake. Therefore, we examined the effects of tiagabine on saccade parameters. Methods: SEV was analyzed in 8 healthy volunteers before and after 7 days of tiagabine treatment. Subjects received tiagabine in a daily dose of 15 mg. Saccades were measured using a noninvasive infrared oculographic device. Amplitude, latency, and SEV were analyzed as a function of treatment and target eccentricity. Results: SEV and saccade latency increased with target amplitude. Treatment with tiagabine had no significant effect on SEV and saccade amplitude. A trend was found for increased latencies after tiagabine. Conclusion: In contrast to findings with benzodiazepines, tiagabine treatment had no impact on SEV in healthy volunteers. The subchronic tolerance effects or the different site of action on the GABA(A)/BZD receptor complex may account for this deviating profile. Copyright (C) 2005 S. Karger AG, Basel

Lagrangian chaos in an ABC--forced nonlinear dynamo

The Lagrangian properties of the velocity field in a magnetized fluid are studied using three-dimensional simulations of a helical magnetohydrodynamic dynamo. We compute the attracting and repelling Lagrangian coherent structures, which are dynamic lines and surfaces in the velocity field that delineate particle transport in flows with chaotic streamlines and act as transport barriers. Two dynamo regimes are explored, one with a robust coherent mean magnetic field and one with intermittent bursts of magnetic energy. The Lagrangian coherent structures and the statistics of finite--time Lyapunov exponents indicate that the stirring/mixing properties of the velocity field decay as a linear function of the magnetic energy. The relevance of this study for the solar dynamo problem is discussed

Vagus nerve stimulation for depression: efficacy and safety in a European study

Background Vagus nerve stimulation (VNS) therapy is associated with a decrease in seizure frequency in partial-onset seizure patients. Initial trials suggest that it may be an effective treatment, with few side-effects, for intractable depression. Method An open, uncontrolled European multi-centre study (D03) of VNS therapy was conducted, in addition to stable pharmacotherapy, in 74 patients with treatment-resistant depression (TRD). Treatment remained unchanged for the first 3 months; in the subsequent 9 months, medications and VNS dosing parameters were altered as indicated clinically. Results The baseline 28-item Hamilton Depression Rating Scale (HAMD-28) score averaged 34. After 3 months of VNS, response rates (50% reduction in baseline scores) reached 37% and remission rates (HAMD-28 score <10) 17%. Response rates increased to 53% after 1 year of VNS, and remission rates reached 33%. Response was defined as sustained if no relapse occurred during the first year of VNS after response onset; 44% of patients met these criteria. Median time to response was 9 months. Most frequent side-effects were voice alteration (63% at 3 months of stimulation) and coughing (23%). Conclusions VNS therapy was effective in reducing severity of depression; efficacy increased over time. Efficacy ratings were in the same range as those previously reported from a USA study using a similar protocol; at 12 months, reduction of symptom severity was significantly higher in the European sample. This might be explained by a small but significant difference in the baseline HAMD-28 score and the lower number of treatments in the current episode in the European stud

Service orchestration with priority constraints

Business process management is an operational management approach that focuses on improving business processes. Business processes, i.e., collections of important activities in an organization, are represented in the form of a workflow, an orchestrated and repeatable pattern of activities amenable to automated analysis and control. Priority is an important concept in modeling workflows. We need priority to model cancelable and compensable tasks within transactional business processes. We use the Reo coordination language to model and formally analyze workflows. In this paper, we propose a constraint-based approach to formalize priority in Reo. We introduce special channels to propagate and block priority flows, define their semantics as constraints, and model priority propagation as a constraint satisfaction problem

Neuroactive steroids in depression and anxiety disorders: Clinical studies

Certain neuroactive steroids modulate ligand-gated ion channels via non-genomic mechanisms. Especially 3 alpha-reduced pregnane steroids are potent positive allosteric modulators of the gamma-aminobutyric acid type A (GABA(A)) receptor. During major depression, there is a disequilibrium of 3 alpha-reduced neuroactive steroids, which is corrected by clinically effective pharmacological treatment. To investigate whether these alterations are a general principle of successful antidepressant treatment, we studied the impact of nonpharmacological treatment options on neuroactive steroid concentrations during major depression. Neither partial sleep deprivation, transcranial magnetic stimulation, nor electroconvulsive therapy affected neuroactive steroid levels irrespectively of the response to these treatments. These studies suggest that the changes in neuroactive steroid concentrations observed after antidepressant pharmacotherapy more likely reflect distinct pharmacological properties of antidepressants rather than the clinical response. In patients with panic disorder, changes in neuroactive steroid composition have been observed opposite to those seen in depression. However, during experimentally induced panic induction either with cholecystokinine-tetrapeptide or sodium lactate, there was a pronounced decline in the concentrations of 3 alpha-reduced neuroactive steroids in patients with panic disorder, which might result in a decreased GABAergic tone. In contrast, no changes in neuroactive steroid concentrations could be observed in healthy controls with the exception of 3 alpha,5 alpha-tetrahydrodeoxycorticosterone. The modulation of GABA(A) receptors by neuroactive steroids might contribute to the pathophysiology of depression and anxiety disorders and might offer new targets for the development of novel anxiolytic compounds. Copyright (c) 2006 S. Karger AG, Basel

On polyhedral projection and parametric programming

Submitted versio