Binary Determinantal Complexity

We prove that for writing the 3 by 3 permanent polynomial as a determinant of a matrix consisting only of zeros, ones, and variables as entries, a 7 by 7 matrix is required. Our proof is computer based and uses the enumeration of bipartite graphs. Furthermore, we analyze sequences of polynomials that are determinants of polynomially sized matrices consisting only of zeros, ones, and variables. We show that these are exactly the sequences in the complexity class of constant free polynomially sized (weakly) skew circuits.Comment: 10 pages, C source code for the computation available as ancillary file

The boundary of the orbit of the 3 by 3 determinant polynomial

We consider the 3 by 3 determinant polynomial and we describe the limit points of the set of all polynomials obtained from the determinant polynomial by linear change of variables. This answers a question of J. M. Landsberg

City and Industry: How to Cross Borders? Learning From Innovative Company Site Transformations

While working and living coexisted in the historical city, the functions are separated in the Modernist city. Recently, the idea of connected urban districts with short distances and attractive work spaces have received renewed attention from companies and planners alike, as soft site factors, tacit knowledge, and local production are gaining importance. In this article we focus on the development of multi-national company sites and the economic and spatial conditions that encourage them to transform existing sites, improve placemaking, and cross borders. We also have a look at their interactive influence on the neighbourhood. We talked to the real estate managers of BASF, BMW, Bosch, Siemens, and Trumpf about site development strategies and approaches for connecting and mixing functions, and therefore crossing borders and, where it is necessary, separating. The professional discourse on "productive cities" and "urban manufacturing" is concerned with reintegrating production into the city. Reurbanisation is especially instrumental in overcoming a major guiding principle or dogma of the Modernist city: the separation of functions. Nevertheless, reurbanisation results in price rises and increases the competition for land. Therefore, planning has to pay attention to industrial areas, as well as housing or the inner-city. An important thesis of the article is that multi-national companies are pioneers in transforming their priority sites to suit future development. For cities, it is an upcoming communal task to ensure that all existing industrial areas develop into "just, green and productive cities," as pointed out in the New Leipzig Charter. To a certain extent, it is possible to adapt the urban planning and design strategies of multi-national companies for existing industrial areas. This is especially true regarding the question of how borders and transition zones between industrial areas of companies and the surrounding neighbourhood can be designed to be spatially and functionally sustainable or how they can be transformed to suit future urban needs. However, urban planning has to balance many concerns and therefore the article concludes with a synopsis of the importance of strategic planning for transforming existing industrial areas

Ein Umweltchemie-Praktikum an der Fachhochschule Darmstadt

It should be an aim of chemical education to make students meet aspects of environmental protection in the lab courses. Students at the Fachhochschule Darmstadt carry out model experiments on metal (Ag, Cu) and polymer (PMMA, PET, PS, paper) recycling and on air and water purification like gas washing, charcoal adsorption, or treatment with H2O2 and UV light. They are made familiar with analytical methods like AAS, UV/VIS spectroscopy and polarography to determine traces of heavy metals in the environment and work on a research project on decontamination of soil

CRL4^(AMBRA1) targets Elongin C for ubiquitination and degradation to modulate CRL5 signaling

Multi‐subunit cullin‐RING ligases (CRLs) are the largest family of ubiquitin E3 ligases in humans. CRL activity is tightly regulated to prevent unintended substrate degradation or autocatalytic degradation of CRL subunits. Using a proteomics strategy, we discovered that CRL4^(AMBRA1) (CRL substrate receptor denoted in superscript) targets Elongin C (ELOC), the essential adapter protein of CRL5 complexes, for polyubiquitination and degradation. We showed that the ubiquitin ligase function of CRL4^(AMBRA1) is required to disrupt the assembly and attenuate the ligase activity of human CRL5^(SOCS3) and HIV‐1 CRL5^(VIF) complexes as AMBRA1 depletion leads to hyperactivation of both CRL5 complexes. Moreover, CRL4^(AMBRA1) modulates interleukin‐6/STAT3 signaling and HIV‐1 infectivity that are regulated by CRL5^(SOCS3) and CRL5^(VIF), respectively. Thus, by discovering a substrate of CRL4^(AMBRA1), ELOC, the shared adapter of CRL5 ubiquitin ligases, we uncovered a novel CRL cross‐regulation pathway

A combined biomarker panel shows improved sensitivity for the early detection of ovarian cancer allowing the identification of the most aggressive Type II tumours.

Background: There is an urgent need for biomarkers for the early detection of ovarian cancer (OC). The purpose of this study was to assess whether changes in serum levels of lecithin-cholesterol acyltransferase (LCAT), sex hormone-binding globulin (SHBG), glucoseregulated protein, 78 kDa (GRP78), calprotectin and insulin-like growth factor-binding protein 2 (IGFBP2) are observed before clinical presentation and to assess the performance of these markers alone and in combination with CA125 for early detection. Methods: This nested case–control study used samples from the United Kingdom Collaborative Trial of Ovarian Cancer Screening trial. The sample set consisted of 482 serum samples from 49 OC subjects and 31 controls, with serial samples spanning up to 7 years pre-diagnosis. The set was divided into the following: (I) a discovery set, which included all women with only two samples from each woman, the first ato14 months and the second at 432 months to diagnosis; and (ii) a corroboration set, which included all the serial samples from the same women spanning the 7-year period. Lecithin-cholesterol acyltransferase, SHBG, GRP78, calprotectin and IGFBP2 were measured using ELISA. The performance of the markers to detect cancers pre-diagnosis was assessed. Results: A combined threshold model IGFBP2 478.5 ng ml 1 : LCAT o8.831 mg ml 1 : CA125 435 Uml 1 outperformed CA125 alone for the earlier detection of OC. The threshold model was able to identify the most aggressive Type II cancers. In addition, it increased the lead time by 5–6 months and identified 26% of Type I subjects and 13% of Type II subjects that were not identified by CA125 alone. Conclusions: Combined biomarker panels (IGFBP2, LCAT and CA125) outperformed CA125 up to 3 years pre-diagnosis, identifying cancers missed by CA125, providing increased diagnostic lead times for Type I and Type II OC. The model identified more aggressive Type II cancers, with women crossing the threshold dying earlier, indicating that these markers can improve on the sensitivity of CA125 alone for the early detection of OC

Translational rodent models for research on parasitic protozoa – a review of confounders and possibilities

Rodents, in particular Mus musculus, have a long and invaluable history as models for human diseases in biomedical research, although their translational value has been challenged in a number of cases. We provide some examples in which rodents have been suboptimal as models for human biology and discuss confounders which influence experiments and may explain some of the misleading results. Infections of rodents with protozoan parasites are no exception in requiring close consideration upon model choice. We focus on the significant differences between inbred, outbred and wild animals, and the importance of factors such as microbiota, which are gaining attention as crucial variables in infection experiments. Frequently, mouse or rat models are chosen for convenience, e.g., availability in the institution rather than on an unbiased evaluation of whether they provide the answer to a given question. Apart from a general discussion on translational success or failure, we provide examples where infections with single-celled parasites in a chosen lab rodent gave contradictory or misleading results, and when possible discuss the reason for this. We present emerging alternatives to traditional rodent models, such as humanized mice and organoid primary cell cultures. So-called recombinant inbred strains such as the Collaborative Cross collection are also a potential solution for certain challenges. In addition, we emphasize the advantages of using wild rodents for certain immunological, ecological, and/or behavioral questions. The experimental challenges (e.g., availability of species-specific reagents) that come with the use of such non-model systems are also discussed. Our intention is to foster critical judgment of both traditional and newly available translational rodent models for research on parasitic protozoa that can complement the existing mouse and rat models

Geometrische Komplexitätstheorie und Bahnabschlüsse homogener Formen

Valiant's Conjecture is the algebraic version of P vs. NP and serves as our central motivation. The first part of the thesis starts out by giving an introduction to the underlying theory. In the second chapter, we define a complexity measure for integer polynomials which can be seen as a discretization of the original theory and can be studied combinatorically. A different approach to Valiant's conjecture is the Geometric Complexity Theory programme (GCT for short) which was introduced in 2001 by Mulmuley and Sohoni. Chapter 3 serves as an introduction to GCT: Here, the separation of complexity classes is reduced to the existence of certain integer vectors, which we also call obstructions. The final chapter of the first part shows that certain obstructions are in some sense rare and only recently, it was confirmed that these obstructions are insufficient to prove Valiant's conjecture via GCT. In the second part of the thesis, we study the central geometric object of GCT in more detail and generality: Given the action of a general linear group on a space of homogeneous polynomials by variable substitution, we are interested in the closure of certain orbits, in particular the orbit of the determinant polynomial. Before we study the determinant, we first analyze the case where the orbit closure contains only polynomials that arise by variable substitution, possibly by a non-invertible transformation. A complete classification of this case remains open, but we can answer and pose serveral questions to advance it. In Chapter 7, we introduce techniques to classify the boundary of orbit closures in the general case. We can successfully give a description for the 3×3 determinant polynomial and under one remaining assumption, also for the general binomial. We also determine the stabilizer group of the determinant of a generic traceless matrix and can conclude that the orbit closure of this polynomial is always an irreducible component of the boundary of the orbit closure of the determinant.Die Vermutung von Valiant ist eine algebraische Version des P vs. NP Problems aus der theoretischen Informatik und unsere zentrale Motivation. Im ersten Teil der Arbeit wird daher zunächst die zugrundeliegende Theorie von Valiant zusammengefasst. Im zweiten Kapitel wird ein Komplexitätsmaß für ganzzahlige Polynome definiert, welches die ursprüngliche Theorie noch stärker diskretisiert und sich rein kombinatorisch untersuchen lässt. Ein anderer Ansatz zur Lösung der Vermutung von Valiant ist die Geometrische Komplexitätstheorie, welche 2001 von Mulmuley und Sohoni ins Leben gerufen wurde: Kapitel 3 der Arbeit liefert eine Einführung. Die Trennung von Komplexitätsklassen wird hier auf die Existenz gewisser ganzzahliger Vektoren mit kombinatorischen Eigenschaften reduziert: Diese Vektoren nennen wir auch Obstruktionen. Im letzten Kapitel des ersten Teils wird gezeigt, dass diese Obstruktionen in einem gewissen Sinne selten sind: Erst kürzlich wurde auch bewiesen, dass diese Obstruktionen tatsächlich nicht ausreichen, um Valiant's Vermutung zu beweisen. Valiant's Conjecture is the algebraic version of P vs. NP and serves as our central motivation. The first part of the thesis begins with an introduction to the underlying theory. Der zweite Teil der Arbeit beschäftigt sich näher und in größerer Allgemeinheit mit dem zentralen Konzept der Geometrischen Komplexitätstheorie: Wir betrachten die Wirkung der allgemeinen linearen Gruppe auf einem Raum homogener Polynome durch Variablensubstitution und studieren den topologischen Abschluss bestimmter Bahnen dieser Wirkung. Zunächst wird der Fall studiert, dass jedes Element in diesem Abschluss durch Variablensubstitution entsteht, möglicherweise mittels einer nicht invertierbaren Transformation. Eine vollständige Klassifikation aller Polynome mit dieser Eigenschaft bleibt offen, obwohl wir einige Fragen im Hinblick darauf beantworten können. Es werden weiterhin Techniken vorgestellt, um den Rand eines Bahnabschlusses auch im Allgemeinen zu klassifizieren. Dies gelingt uns für den Fall der 3×3 Determinante und unter einer verbleibenden Annahme auch für das allgemeine Binom. Wir bestimmen hier auch den Stabilisator der Determinante einer allgemeinen, spurlosen Matrix und können schlussfolgern, dass der Bahnabschluss dieses Polynoms stets eine irreduzible Komponente im Rand des Bahnabschlusses der allgemeinen Determinante ist. Der Determinante gilt hier besondere Aufmerksamkeit aufgrund ihrer wichtigen Rolle in der algebraischen Komplexitätstheorie.DFG, BU 1371/2-2, Geglättete Analyse von KonditionszahlenDFG, BU 1371/3-2, Geometrische Komplexitätstheori