Disjoint essential sets of implicates of a CQ Horn function

In this paper we study a class of CQ Horn functions introduced in Boros et al. (Ann Math Artif Intell 57(3–4):249–291, 2010). We prove that given a CQ Horn function f, the maximal number of pairwise disjoint essential sets of implicates of f equals the minimum number of clauses in a CNF representing f. In other words, we prove that the maximum number of pairwise disjoint essential sets of implicates of f constitutes a tight lower bound on the size (the number of clauses) of any CNF representation of f.     

Optimization problems in contracted tensor networks

We discuss the calculus of variations in tensor representations with a special focus on tensor networks and apply it to functionals of practical interest. The survey provides all necessary ingredients for applying minimization methods in a general setting. The important cases of target functionals which are linear and quadratic with respect to the tensor product are discussed, and combinations of these functionals are presented in detail. As an example, we consider the representation rank compression in tensor networks. For the numerical treatment, we use the nonlinear block Gauss?CSeidel method. We demonstrate the rate of convergence in numerical tests.     

Convex combinations of strict t-norms

Alsina, Frank, and Schweizer posed a question whether a non-trivial convex combination of triangular norms can ever be a triangular norm. In this paper we deal with the class of strict t-norms with well-defined first partial derivatives along their zero borders. We show that the answer to the question is negative for certain couples of such t-norms and we state out possible further research.     

Rechtliche Fragen zur Praxis IT-forensischer Analysen in Organisationen

Der Einsatz von Informationstechnologie (IT) in Organisationen bietet viele M?glichkeiten des Missbrauchs. Besch?ftigte k?nnen sich die besonderen Eigenschaften der IT zunutze machen, um sich etwa in gesch?ftssch?digender Weise Vorteile zu verschaffen. Gleichzeitig erm?glicht IT aber auch, verbotene Handlungen aufzuspüren und zu belegen (IT-Forensik). Der Beitrag beschreibt die technische Praxis von IT-forensischen Analysen und geht auf damit verbundene rechtliche Fragestellungen ein.     

Estimation of time-dependent input from neuronal membrane potential

The set of firing rates of the presynaptic excitatory and inhibitory neurons constitutes the input signal to the postsynaptic neuron. Estimation of the time-varying input rates from intracellularly recorded membrane potential is investigated here. For that purpose, the membrane potential dynamics must be specified. We consider the Ornstein-Uhlenbeck stochastic process, one of the most common single-neuron models, with time-dependent mean and variance. Assuming the slow variation of these two moments, it is possible to formulate the estimation problem by using a state-space model. We develop an algorithm that estimates the paths of the mean and variance of the input current by using the empirical Bayes approach. Then the input firing rates are directly available from the moments. The proposed method is applied to three simulated data examples: constant signal, sinusoidally modulated signal, and constant signal with a jump. For the constant signal, the estimation performance of the method is comparable to that of the traditionally applied maximum likelihood method. Further, the proposed method accurately estimates both continuous and discontinuous time-variable signals. In the case of the signal with a jump, which does not satisfy the assumption of slow variability, the robustness of the method is verified. It can be concluded that the method provides reliable estimates of the total input firing rates, which are not experimentally measurable.     

ALTDSE: An Arnoldi–Lanczos program to solve the time-dependent Schrödinger equation

We describe a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom. While the field-free Hamiltonian and the dipole matrices may be generated using an arbitrary primitive basis, they are assumed to have been transformed to the eigenbasis of the problem before the solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. Probabilities for survival of the ground state, excitation, and single ionization can be extracted from the propagated wavefunction.

Program summary

Program title: ALTDSECatalogue identifier: AEDM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2154No. of bytes in distributed program, including test data, etc.: 30 827Distribution format: tar.gzProgramming language: Fortran 95. [A Fortran 2003 call to “flush” is used to simplify monitoring the output file during execution. If this function is not available, these statements should be commented out.].Computer: Shared-memory machinesOperating system: Linux, OpenMPHas the code been vectorized or parallelized?: YesRAM: Several Gb, depending on matrix size and number of processorsSupplementary material: To facilitate the execution of the program, Hamiltonian field-free and dipole matrix files are provided.Classification: 2.5External routines: LAPACK, BLASNature of problem: We describe a computer program for a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom [1,2]. The probabilities for survival of the initial state, excitation of discrete states, and single ionization due to multi-photon processes can be obtained.Solution method: The solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. The field-free Hamiltonian and the dipole matrices, originally generated in an arbitrary basis (e.g., the flexible B-spline R-matrix (BSR) method with non-orthogonal orbitals [3]), must be provided in the eigenbasis of the problem as input.Restrictions: The present program is restricted to a ¹S^e initial state and linearly polarized light. This is the most common situation experimentally, but a generalization is straightforward.Running time: Several hours, depending on the number of threads used.References: [1] X. Guan, O. Zatsarinny, K. Bartschat, B.I. Schneider, J. Feist, C.J. Noble, Phys. Rev. A 76 (2007) 053411. [2] X. Guan, C.J. Noble, O. Zatsarinny, K. Bartschat, B.I. Schneider, Phys. Rev. A 78 (2008) 053402. [3] O. Zatsarinny, Comput. Phys. Comm. 174 (2006) 273.     

The Complexity of Hybrid Logics over Equivalence Relations

This paper examines and classifies the computational complexity of model checking and satisfiability for hybrid logics over frames with equivalence relations. The considered languages contain all possible combinations of the downarrow binder, the existential binder, the satisfaction operator, and the global modality, ranging from the minimal hybrid language to very expressive languages. For model checking, we separate polynomial-time solvable from PSPACE-complete cases, and for satisfiability, we exhibit cases complete for NP, PSpace, NExpTime, and even N2ExpTime. Our analysis includes the versions of all these languages without atomic propositions, and also complete frames.     

Parsing human skeletons in an operating room

Multiple human pose estimation is an important yet challenging problem. In an operating room (OR) environment, the 3D body poses of surgeons and medical staff can provide important clues for surgical workflow analysis. For that purpose, we propose an algorithm for localizing and recovering body poses of multiple human in an OR environment under a multi-camera setup. Our model builds on 3D Pictorial Structures and 2D body part localization across all camera views, using convolutional neural networks (ConvNets). To evaluate our algorithm, we introduce a dataset captured in a real OR environment. Our dataset is unique, challenging and publicly available with annotated ground truths. Our proposed algorithm yields to promising pose estimation results on this dataset.