APPROXIMATING SEPARABLE NONLINEAR FUNCTIONS VIA MIXED ZERO-ONE PROGRAMS

We discuss two models from the literature that have been developed to formulate piecewise linear approximation of separable nonlinear functions by way of mixed-integer programs. We show that the most commonly proposed method is computationally inferior to a lesser known technique by comparing analytically the linear programming relaxations of the two formulations. A third way of formulating the problem, that shares the advantages of the better of the two known methods, is also proposed.Statistics Working Papers Serie

Alternative Methods of Linear Regression

This paper is a survey on traditional linear regression techniques using the lñ-, l2-, and lâÂÂ-norm. We derive the characterization of the respective regression estimates (including optimality and uniqueness criteria), as well as discuss some of their statistical properties.Statistics Working Papers Serie

APPROXIMATING SEPARABLE NONLINEAR FUNCTIONS VIA MIXED ZERO-ONE PROGRAMS

We discuss two models from the literature that have been developed to formulate piecewise linear approximation of separable nonlinear functions by way of mixed-integer programs. We show that the most commonly proposed method is computationally inferior to a lesser known technique by comparing analytically the linear programming relaxations of the two formulations. A third way of formulating the problem, that shares the advantages of the better of the two known methods, is also proposed.Statistics Working Papers Serie

Does Automated Unit Test Generation Really Help Software Testers? A Controlled Empirical Study

Work on automated test generation has produced several tools capable of generating test data which achieves high structural coverage over a program. In the absence of a specification, developers are expected to manually construct or verify the test oracle for each test input. Nevertheless, it is assumed that these generated tests ease the task of testing for the developer, as testing is reduced to checking the results of tests. While this assumption has persisted for decades, there has been no conclusive evidence to date confirming it. However, the limited adoption in industry indicates this assumption may not be correct, and calls into question the practical value of test generation tools. To investigate this issue, we performed two controlled experiments comparing a total of 97 subjects split between writing tests manually and writing tests with the aid of an automated unit test generation tool, EvoSuite. We found that, on one hand, tool support leads to clear improvements in commonly applied quality metrics such as code coverage (up to 300% increase). However, on the other hand, there was no measurable improvement in the number of bugs actually found by developers. Our results not only cast some doubt on how the research community evaluates test generation tools, but also point to improvements and future work necessary before automated test generation tools will be widely adopted by practitioners

There is no magic in speaker policies : creating gender equality at brain stimulation conferences Editorial II to the supplement from the 2nd European Conference on brain stimulation in psychiatry

Non peer reviewe

Claw-free t-perfect graphs can be recognised in polynomial time

A graph is called t-perfect if its stable set polytope is defined by non-negativity, edge and odd-cycle inequalities. We show that it can be decided in polynomial time whether a given claw-free graph is t-perfect

Alternative Methods of Linear Regression

This paper is a survey on traditional linear regression techniques using the lñ-, l2-, and lâÂÂ-norm. We derive the characterization of the respective regression estimates (including optimality and uniqueness criteria), as well as discuss some of their statistical properties.Statistics Working Papers Serie

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