Nicht konstruktiv beweisbare Sätze der Analysis

Nach allgemeiner Ueberzeugung können gewisse Sätze der Analysis nicht konstruktiv bewiesen werden. Man denke etwa an den folgenden Satz: Eine monotone und beschränkte Folge a(n) von rationalen Zahlen konvergiert, d.h. es gibt eine solche ganzzahlige Funktion k(m), daß Unter einem konstruktiven Beweis dieses Satzes hätte man etwa die Angabe eines Verfahrens zu verstehen, das gestattet, die Funktion k(m) auf Grand der Folge a(n) rekursiv zu definieren. Wenn ein solcher Beweis vorläge, wäre insbesondere gezeigt, daß es zu einer rekursiv definierten Folge a(n) mit den verlangten Eigenschaften stets eine rekursiv definierbare Konvergenzfunktion k(m) gibt. Es soil nun im folgenden von einigen grundlegenden Sätzen der reellen Analysis gezeigt werden, daß sie nicht konstruktiv bewiesen werden können—konstruktiv in dem Sinn, der eben angedeutet wurde. Wir stützen uns dabei auf die Begriffe der rekursiven und der berechenbaren Funktion; rekursive und berechenbare Funktionen sind zahlentheoretische Funktionen. Unter einer rekursiven Funktion möge vorläufig eine primitiv rekursive Funktion verstanden werden (vgl. etwa D. Hilbert und P. Bernays [3], S.286); berechenbar meint berechenbar im Sinne von A. Church [1], S. C. Kleene [4], A. M. Turing [6]. Der Begriff der "konstruktiv definierten Funktion” wird durch die Bestimmung als "rekursive Funktion” eher eng, durch die Bestimmung als "berechenbare Funktion” eher weit gefaßt. Definition I. Eine Folge rationaler Zahlen Φ(n) heißt rekursiv,(berechenbar), wenn es solche rekursiven (berechenbaren) Funktionen ϕ{n), ψ(n) und χ(n) gibt, daß χ(n) ≧1 und . Definition II. Eine Folge Φ(n) von rationalen Zahlen heißt rekursiv (berechenbar) konvergent, wenn es eine solche rekursive (berechenbare) Funktion v(m) gibt, daß Wir werden zeigen (Satz I): Es gibt eine rekursive, monotone und beschränkte Folge rationaler Zahlen, die nicht berechenbar konvergiert. Bei unserer Auffassungsweise ist darin enthalten, daß der zu Beginn erwähnte Satz nicht konstruktiv bewiesen werden kan

A Realistic Predictor for Pedestrian Attribute Recognition

The application of video surveillance systems in public areas to ensure public security is becoming increasingly important. A major task when evaluating the arising amount of video data is to find the occurrences of a person-of-interest on the basis of a testimony. For the comparison of a person’s description with persons in the video data, the attributes of all persons must be recognized automatically. However, typical approaches to pedestrian attribute recognition simply predict all attributes for a person, regardless the visibility of relevant attributes. To address this problem, the concept of realistic predictors is used in this work to determine and improve the reliability of pedestrian attribute recognition

South Dakota Pregnancy Risk Assessment Monitoring System (PRAMS)

The Pregnancy Risk Assessment Monitoring System (PRAMS) was developed by the Centers for Disease Control and Prevention (CDC) in 1987 and is done in collaboration with various state health departments. PRAMS is a statewide survey that collects valuable information from new mothers to find out why some babies are born healthy and others are not. The PRAMS provides state agencies and the CDC with data so they can monitor changes in maternal and child health indicators such as the prevalence of unintended pregnancy, prenatal care, breastfeeding, and smoking and drinking behaviors. PRAMS data can be used to identify groups of women and children who are at high risk for health problems and to measure the progress of goals that are developed to improve the health of women and children. PRAMS data also can be used by researchers to investigate emerging issues of maternal and child health, by state and local governments to design or review maternal and child health programs and policies, and by state agencies to help plan maternal and child health programs. Currently forty states and New York City participate in the PRAMS, representing approximately 78% of all U.S. live births. The Ethel Austin Martin Program at South Dakota State University, in partnership with the South Dakota Department of Health, is conducting the state’s first-ever statewide PRAMS

A Transformer based Multi task Model for Attribute based Person Retrieval

Person retrieval is a crucial task in video surveillance. While searching for persons-of-interest based on so-called query images gains much interest in the research community, attribute-based approaches are rarely studied. Attribute-based person retrieval takes a person’s semantic attributes as input and provides a ranked list of search results that match the description. Typically, such approaches either build on a pedestrian attribute recognition approach or learn a joint feature space between attribute descriptions and image data. In this work, both approaches are combined in a multi-task model to benefit from the advantages of both procedures. Moreover, transformer modules are incorporated to increase performance further. Experimental evaluation proves the effectiveness of the approach and shows that the proposed architecture outperforms the baselines significantly

Session 11: \u3cem\u3eData and Epidemiology: The Need to Educate the Public\u3c/em\u3e

Unlike previous pandemics, the COVID pandemic came at a time of political polarization and extensive use of social media. Early in the outbreak, it soon became clear that the general lack of understanding of simple epidemiologic principles led to confusion and mistrust. Using data posted to the South Dakota Department of Health dashboard, summaries of daily data were provided via email and blog to individuals from university emergency management staff to city council members, retirees, and the general public. Weekly videos were produced by the city and posted to social media accounts. The goal of these data updates and videos was to provide graphic summaries of the current situation in Brookings County and the state of South Dakota and educate the public on the general principles of epidemiology

Tones of the Times: Reflections on the 2021 Alpentöne Festival with Barbara Betschart, Roland Dahinden, Pius Knüsel, and Roland Schiltknecht. Altdorf, August 2021

The town of Altdorf in Uri, Switzerland is home to the biennial Alpentöne Festival. The most recent iteration took place, live and on-site, in August 2021. Sharon Specker speaks with four people involved in its realization: Barbara Betschart, one of the artistic directors; Pius Knüsel, the executive director, Roland Dahinden, trombonist and composer; and Roland Schiltknecht, hammered dulcimer player.The town of Altdorf in Uri, Switzerland is home to the biennial Alpentöne Festival. The most recent iteration took place, live and on-site, in August 2021. Sharon Specker speaks with four people involved in its realization: Barbara Betschart, one of the artistic directors; Pius Knüsel, the executive director, Roland Dahinden, trombonist and composer; and Roland Schiltknecht, hammered dulcimer player.The town of Altdorf in Uri, Switzerland is home to the biennial Alpentöne Festival. The most recent iteration took place, live and on-site, in August 2021. Sharon Specker speaks with four people involved in its realization: Barbara Betschart, one of the artistic directors; Pius Knüsel, the executive director, Roland Dahinden, trombonist and composer; and Roland Schiltknecht, hammered dulcimer player.The town of Altdorf in Uri, Switzerland is home to the biennial Alpentöne Festival. The most recent iteration took place, live and on-site, in August 2021. Sharon Specker speaks with four people involved in its realization: Barbara Betschart, one of the artistic directors; Pius Knüsel, the executive director, Roland Dahinden, trombonist and composer; and Roland Schiltknecht, hammered dulcimer player

Influence of Rapid Growth on Skeletal Adaptation to Exercise

During rapid growth, increased body weight and muscle strength result in increased loads on bone. Bone adapts to these increased strains by increasing bone modeling and remodeling. As the growth rate decreases, bone that was formed as a result of these adaptations continues to mineralize and catch up , and bone modeling and remodeling decreases. Bone benefits of exercise in childhood are reported in some studies, although we observed less BMC gain at trabecular-rich sites during the peri-pubertal period in children who jumped than those who did not. Data from 13 existing pediatric exercise studies were compiled to determine whether similar patterns of age-related bone changes could be identified, and whether the bone benefit of exercise differed depending upon pubertal stage. The benefit of exercise on total body BMC gains occurred across all ages, whereas greater exercise-induced gains at the spine and hip were observed in younger children compared to older children. The majority of studies found a positive effect of exercise on bone, but typically this involved limiting the analysis to specific sub-populations (i.e., higher calcium intake, lower baseline activity levels, smaller body size). Limitations of the studies published to date are discussed