Singular 0/1-matrices, and the hyperplanes spanned by random 0/1-vectors

Let $P(d)$ be the probability that a random 0/1-matrix of size $d \times d$ is singular, and let $E(d)$ be the expected number of 0/1-vectors in the linear subspace spanned by d-1 random independent 0/1-vectors. (So $E(d)$ is the expected number of cube vertices on a random affine hyperplane spanned by vertices of the cube.) We prove that bounds on $P(d)$ are equivalent to bounds on $E(d)$: $$P(d) = (2^{-d} E(d) + \frac{d^2}{2^{d+1}}) (1 + o(1)).$$ We also report about computational experiments pertaining to these numbers.Comment: 9 page

Deciding First-Order Satisfiability when Universal and Existential Variables are Separated

We introduce a new decidable fragment of first-order logic with equality, which strictly generalizes two already well-known ones -- the Bernays-Sch\"onfinkel-Ramsey (BSR) Fragment and the Monadic Fragment. The defining principle is the syntactic separation of universally quantified variables from existentially quantified ones at the level of atoms. Thus, our classification neither rests on restrictions on quantifier prefixes (as in the BSR case) nor on restrictions on the arity of predicate symbols (as in the monadic case). We demonstrate that the new fragment exhibits the finite model property and derive a non-elementary upper bound on the computing time required for deciding satisfiability in the new fragment. For the subfragment of prenex sentences with the quantifier prefix $\exists^* \forall^* \exists^*$ the satisfiability problem is shown to be complete for NEXPTIME. Finally, we discuss how automated reasoning procedures can take advantage of our results.Comment: Extended version of our LICS 2016 conference paper, 23 page

Working towards an Improved Monitoring Infrastructure to support Disaster Management, Humanitarian Relief and Civil Security

Within this paper experiences and results from the work in the context of the European Initiative on Global Monitoring for Environment and Security (GMES) as they were gathered within the German Remote Sensing Data Center (DFD) are reported. It is described how data flows, analysis methods and information networks can be improved to allow better and faster access to remote sensing data and information in order to support the management of crisis situations. This refers to all phases of a crisis or disaster situation, including preparedness, response and recovery. Above the infrastructure and information flow elements, example cases of different crisis situations in the context of natural disasters, humanitarian relief activities and civil security are discussed. This builds on the experiences gained during the very active participation in the network of Excellence on Global Monitoring for Stability and Security (GMOSS), the GMES Service Element RESPOND, focussing on Humanitarian Relief Support and supporting the International Charter on Space and Major Disasters as well as while linking closely to national, European and international entities related to civil human security. It is suggested to further improve the network of national and regional centres of excellence in this context in order to improve local, regional and global monitoring capacities. Only when optimum interoperability and information flow can be achieved among systems and data providers on one hand side and the decision makers on the other, efficient monitoring and analysis capacities can be established successfully

Hybrid parallelization of an adaptive finite element code

summary:We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition for both, the large problem and the smaller sub-problems, sufficiently fast we make use of a hierarchical mesh structure. The partitioning is done on a coarser mesh level, resulting in a very fast method that shows good computational balancing results. Numerical experiments show that both parallelization methods achieve good scalability in computing solution of nonlinear, time dependent, higher order PDEs on large domains. The parallelization is realized in the adaptive finite element software AMDiS

Contribution of GABAergic Interneurons to the Development of Spontaneous Activity Patterns in Cultured Neocortical Networks

Periodic synchronized events are a hallmark feature of developing neuronal networks and are assumed to be crucial for the maturation of the neuronal circuitry. In the developing neocortex, the early network oscillations coincide with an excitatory action of the neurotransmitter gamma-aminobutyric acid (GABA). A relationship between the emerging inhibitory action of GABA and the gradual disappearance of early synchronized network activity has been previously suggested. Therefore we investigate the interplay between the action of GABA and spontaneous activity in cultured networks of the lateral or dorsal embryonic rat neocortex, which show considerable difference in the content of GABAergic neurons. Here we present the results of long-term monitoring of spontaneous electrical activity of cultured networks growing on microelectrode arrays and the time course of changes in GABA action using calcium imaging. All cultures studied displayed stereotyped synchronized burst events at the end of the first week in vitro. As the GABAA depolarizing action decreases, naturally or after bumetanide treatment, network activity in lateral cortex cultures changed from stereotypic bursting to more clustered and asynchronous activity patterns. Dorsal cortex cultures and cultures lacking GABAA-receptor mediated synaptic transmission, retained an immature synchronous firing pattern, but developed prominent intraburst oscillations (∼3–10 Hz). Large, mostly parvalbumin positive, GABAergic neurons dominate the GABAergic population in lateral cortex cultures. These large interneurons were virtually absent in dorsal cortex cultures. Based on these results, we suggest that the richly interconnected large GABAergic neurons contribute to desynchronize and temporally differentiate the spontaneous activity of cultured cortical networks

SMIX: Self-managing indexes for dynamic workloads

As databases accumulate growing amounts of data at an increasing rate, adaptive indexing becomes more and more important. At the same time, applications and their use get more agile and flexible, resulting in less steady and less predictable workload characteristics. Being inert and coarse-grained, state-of-the-art index tuning techniques become less useful in such environments. Especially the full-column indexing paradigm results in many indexed but never queried records and prohibitively high storage and maintenance costs. In this paper, we present Self-Managing Indexes, a novel, adaptive, fine-grained, autonomous indexing infrastructure. In its core, our approach builds on a novel access path that automatically collects useful index information, discards useless index information, and competes with its kind for resources to host its index information. Compared to existing technologies for adaptive indexing, we are able to dynamically grow and shrink our indexes, instead of incrementally enhancing the index granularity

Improved MSSM Higgs mass calculation using the 3-loop FlexibleEFTHiggs approach including xtx_t-resummation

We present an improved calculation of the light CP-even Higgs boson pole mass in the MSSM based on the FlexibleEFTHiggs hybrid method. The calculation resums large logarithms to all orders and includes power-suppressed terms at fixed order. It uses state-of-the-art 2- and 3-loop matching of the quartic Higgs coupling and renormalization group running up to 4-loop, resulting in a resummation of large logarithmic corrections up to N$^3$LL level. A conceptually novel ingredient is the expansion of the matching conditions in terms of high-scale MSSM parameters instead of SM parameters. In this way leading terms in the stop-mixing parameter are effectively resummed, leading to an improved numerical convergence of the perturbative expansion. Furthermore, the avoidance of double counting of loop corrections is more transparent than in other approaches and more independent of the high-scale model. We present numerical results and a detailed discussion of theoretical uncertainties for standard benchmark scenarios.Comment: 57 page