Parametric, nonparametric and parametric modelling of a chaotic circuit time series

The determination of a differential equation underlying a measured time series is a frequently arising task in nonlinear time series analysis. In the validation of a proposed model one often faces the dilemma that it is hard to decide whether possible discrepancies between the time series and model output are caused by an inappropriate model or by bad estimates of parameters in a correct type of model, or both. We propose a combination of parametric modelling based on Bock's multiple shooting algorithm and nonparametric modelling based on optimal transformations as a strategy to test proposed models and if rejected suggest and test new ones. We exemplify this strategy on an experimental time series from a chaotic circuit where we obtain an extremely accurate reconstruction of the observed attractor.Comment: 19 pages, 8 Fig

Almost Perfect Privacy for Additive Gaussian Privacy Filters

We study the maximal mutual information about a random variable $Y$ (representing non-private information) displayed through an additive Gaussian channel when guaranteeing that only $\epsilon$ bits of information is leaked about a random variable $X$ (representing private information) that is correlated with $Y$. Denoting this quantity by $g_\epsilon(X,Y)$, we show that for perfect privacy, i.e., $\epsilon=0$, one has $g_0(X,Y)=0$ for any pair of absolutely continuous random variables $(X,Y)$ and then derive a second-order approximation for $g_\epsilon(X,Y)$ for small $\epsilon$. This approximation is shown to be related to the strong data processing inequality for mutual information under suitable conditions on the joint distribution $P_{XY}$. Next, motivated by an operational interpretation of data privacy, we formulate the privacy-utility tradeoff in the same setup using estimation-theoretic quantities and obtain explicit bounds for this tradeoff when $\epsilon$ is sufficiently small using the approximation formula derived for $g_\epsilon(X,Y)$.Comment: 20 pages. To appear in Springer-Verla

Gaussian Bounds for Noise Correlation of Functions

In this paper we derive tight bounds on the expected value of products of {\em low influence} functions defined on correlated probability spaces. The proofs are based on extending Fourier theory to an arbitrary number of correlated probability spaces, on a generalization of an invariance principle recently obtained with O'Donnell and Oleszkiewicz for multilinear polynomials with low influences and bounded degree and on properties of multi-dimensional Gaussian distributions. The results derived here have a number of applications to the theory of social choice in economics, to hardness of approximation in computer science and to additive combinatorics problems.Comment: Typos and references correcte

Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR

Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials (mu_B > 500 MeV), effects of chiral symmetry, and the equation-of-state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2022, in the context of the worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal

Contribution of Distinct Homeodomain DNA Binding Specificities to Drosophila Embryonic Mesodermal Cell-Specific Gene Expression Programs

Homeodomain (HD) proteins are a large family of evolutionarily conserved transcription factors (TFs) having diverse developmental functions, often acting within the same cell types, yet many members of this family paradoxically recognize similar DNA sequences. Thus, with multiple family members having the potential to recognize the same DNA sequences in cis-regulatory elements, it is difficult to ascertain the role of an individual HD or a subclass of HDs in mediating a particular developmental function. To investigate this problem, we focused our studies on the Drosophila embryonic mesoderm where HD TFs are required to establish not only segmental identities (such as the Hox TFs), but also tissue and cell fate specification and differentiation (such as the NK-2 HDs, Six HDs and identity HDs (I-HDs)). Here we utilized the complete spectrum of DNA binding specificities determined by protein binding microarrays (PBMs) for a diverse collection of HDs to modify the nucleotide sequences of numerous mesodermal enhancers to be recognized by either no or a single subclass of HDs, and subsequently assayed the consequences of these changes on enhancer function in transgenic reporter assays. These studies show that individual mesodermal enhancers receive separate transcriptional input from both I–HD and Hox subclasses of HDs. In addition, we demonstrate that enhancers regulating upstream components of the mesodermal regulatory network are targeted by the Six class of HDs. Finally, we establish the necessity of NK-2 HD binding sequences to activate gene expression in multiple mesodermal tissues, supporting a potential role for the NK-2 HD TF Tinman (Tin) as a pioneer factor that cooperates with other factors to regulate cell-specific gene expression programs. Collectively, these results underscore the critical role played by HDs of multiple subclasses in inducing the unique genetic programs of individual mesodermal cells, and in coordinating the gene regulatory networks directing mesoderm development.National Institutes of Health (U.S.) (Grant R01 HG005287

Alignment of the ALICE Inner Tracking System with cosmic-ray tracks

37 pages, 15 figures, revised version, accepted by JINSTALICE (A Large Ion Collider Experiment) is the LHC (Large Hadron Collider) experiment devoted to investigating the strongly interacting matter created in nucleus-nucleus collisions at the LHC energies. The ALICE ITS, Inner Tracking System, consists of six cylindrical layers of silicon detectors with three different technologies; in the outward direction: two layers of pixel detectors, two layers each of drift, and strip detectors. The number of parameters to be determined in the spatial alignment of the 2198 sensor modules of the ITS is about 13,000. The target alignment precision is well below 10 micron in some cases (pixels). The sources of alignment information include survey measurements, and the reconstructed tracks from cosmic rays and from proton-proton collisions. The main track-based alignment method uses the Millepede global approach. An iterative local method was developed and used as well. We present the results obtained for the ITS alignment using about 10^5 charged tracks from cosmic rays that have been collected during summer 2008, with the ALICE solenoidal magnet switched off.Peer reviewe

Gli3 utilizes Hand2 to synergistically regulate tissue-specific transcriptional networks.

Despite a common understanding that Gli TFs are utilized to convey a Hh morphogen gradient, genetic analyses suggest craniofacial development does not completely fit this paradigm. Using the mouse model (Mus musculus), we demonstrated that rather than being driven by a Hh threshold, robust Gli3 transcriptional activity during skeletal and glossal development required interaction with the basic helix-loop-helix TF Hand2. Not only did genetic and expression data support a co-factorial relationship, but genomic analysis revealed that Gli3 and Hand2 were enriched at regulatory elements for genes essential for mandibular patterning and development. Interestingly, motif analysis at sites co-occupied by Gli3 and Hand2 uncovered mandibular-specific, low-affinity, \u27divergent\u27 Gli-binding motifs (dGBMs). Functional validation revealed these dGBMs conveyed synergistic activation of Gli targets essential for mandibular patterning and development. In summary, this work elucidates a novel, sequence-dependent mechanism for Gli transcriptional activity within the craniofacial complex that is independent of a graded Hh signal

MAGE I Transcription Factors Regulate KAP1 and KRAB Domain Zinc Finger Transcription Factor Mediated Gene Repression

Class I MAGE proteins (MAGE I) are normally expressed only in developing germ cells but are aberrantly expressed in many cancers. They have been shown to promote tumor survival, aggressive growth, and chemoresistance but the underlying mechanisms and MAGE I functions have not been fully elucidated. KRAB domain zinc finger transcription factors (KZNFs) are the largest group of vertebrate transcription factors and regulate neoplastic transformation, tumor suppression, cellular proliferation, and apoptosis. KZNFs bind the KAP1 protein and direct KAP1 to specific DNA sequences where it suppresses gene expression by inducing localized heterochromatin characterized by histone 3 lysine 9 trimethylation (H3me3K9). Discovery that MAGE I proteins also bind to KAP1 prompted us to investigate whether MAGE I can affect KZNF and KAP1 mediated gene regulation. We found that expression of MAGE I proteins, MAGE-A3 or MAGE-C2, relieved repression of a reporter gene by ZNF382, a KZNF with tumor suppressor activity. ChIP of MAGE I (-) HEK293T cells showed KAP1 and H3me3K9 are normally bound to the ID1 gene, a target of ZNF382, but that binding is greatly reduced in the presence of MAGE I proteins. MAGE I expression relieved KAP1 mediated ID1 repression, causing increased expression of ID1 mRNA and ID1 chromatin relaxation characterized by loss of H3me3K9. MAGE I binding to KAP1 also induced ZNF382 poly-ubiquitination and degradation, consistent with loss of ZNF382 leading to decreased KAP1 binding to ID1. In contrast, MAGE I expression caused increased KAP1 binding to Ki67, another KAP1 target gene, with increased H3me3K9 and decreased Ki67 mRNA expression. Since KZNFs are required to direct KAP1 to specific genes, these results show that MAGE I proteins can differentially regulate members of the KZNF family and KAP1 mediated gene repression