Zeno machines and hypercomputation

This paper reviews the Church-Turing Thesis (or rather, theses) with reference to their origin and application and considers some models of "hypercomputation", concentrating on perhaps the most straight-forward option: Zeno machines (Turing machines with accelerating clock). The halting problem is briefly discussed in a general context and the suggestion that it is an inevitable companion of any reasonable computational model is emphasised. It is hinted that claims to have "broken the Turing barrier" could be toned down and that the important and well-founded role of Turing computability in the mathematical sciences stands unchallenged.Comment: 11 pages. First submitted in December 2004, substantially revised in July and in November 2005. To appear in Theoretical Computer Scienc

www.springerreference.com/docs/html/chapterdbid/60497.html Mechanical Computing: The Computational Complexity of Physical Devices

- Mechanism: A machine or part of a machine that performs a particular task computation: the use of a computer for calculation.- Computable: Capable of being worked out by calculation, especially using a computer.- Simulation: Used to denote both the modeling of a physical system by a computer as well as the modeling of the operation of a computer by a mechanical system; the difference will be clear from the context. Definition of the Subject Mechanical devices for computation appear to be largely displaced by the widespread use of microprocessor-based computers that are pervading almost all aspects of our lives. Nevertheless, mechanical devices for computation are of interest for at least three reasons: (a) Historical: The use of mechanical devices for computation is of central importance in the historical study of technologies, with a history dating back thousands of years and with surprising applications even in relatively recent times. (b) Technical & Practical: The use of mechanical devices for computation persists and has not yet been completely displaced by widespread use of microprocessor-based computers. Mechanical computers have found applications in various emerging technologies at the micro-scale that combine mechanical functions with computational and control functions not feasible by purely electronic processing. Mechanical computers also have been demonstrated at the molecular scale, and may also provide unique capabilities at that scale. The physical designs for these modern micro and molecular-scale mechanical computers may be based on the prior designs of the large-scale mechanical computers constructed in the past. (c) Impact of Physical Assumptions on Complexity of Motion Planning, Design, and Simulation: The study of computation done by mechanical devices is also of central importance in providing lower bounds on the computational resources such as time and/or space required to simulate a mechanical syste

Proceedings: Aeronautics and Space Science

VARIABILITY IN AGN ABSORPTION LINES BASED ON HUBBLE SPACE TELESCOPE/COS DATA BALQSO KINETIC LUMINOSITY DETERMINATION WITH C III* MEASUREMENTS BREWSTER ANGLE MICROSCOPY AND CHARACTERIZATIONS OF LANGMUIR FILMS SORTING LIGHT’S TOTAL ANGULAR MOMENTUM FOR COMMUNICATION SYSTEMS THE PHOSPHORYLATION PATTERN OF RPA2, IN RESPONSE TO DOUBLE-STRAND BREAKS, DIFFERS DEPENDING ON THE LOCATION IN THE CELL AND THE PHASE OF THE CELL CYCLE THE DIOPHANTINE EQUATION Ax^4+By^4=Cz^4 IN QUADRATIC FIELDS THE SBML STANDARD TO SHARE COMPUTATIONAL MODELS OF BIOLOGICAL SYSTEMS HIGH SPEED ELECTRO-DISCHARGE DRILLING AND WIRE ELECTRODE-DISCHARGE MACHINING OF TITANIUM ALLOYS FOR AEROSPACE APPLICATIONS ROUTING OVER THE INTERPLANETARY INTERNET WIRELESS INTEGRATED RELAY SYSTEM (WIRS) HUMAN REACTIONS TO FLUCTUATING NOISE CONDITIONS AS PRODUCED BY LOW-BOOM SUPERSONIC AIRCRAFT NONINVASIVE, AMBULATORY, LONG-TERM, DEEP GASTROINTESTINAL BIOSENSOR AND IMPLANTER RECONFIGURATION PLANNING OF MODULAR ROBOT UNDER UNCERTAINTY DYNAMIC GAIT ADAPTION IN FIXED CONFIGURATION FOR MODULAR SELF-RECONFIGURABLE ROBOTS USING FUZZY LOGIC CONTROL EARLY STAGE DEVELOPMENT OF A MEDICAL DEVICE FOR NON-INVASIVE MEASUREMENT OF INTRACRANIAL PRESSURE COMPLIANT LAPAROSCOPIC SURGICAL GRASPER MODULAR JOYSTICK FOR VIRTUAL REALITY SURGICAL SIMULATION NOVEL ASSISTIVE LOCOMOTOR TOOL FOR GAIT REHABILITATION IN THE ELDERLY GAIT VARIABILITY HAS NO RELATION TO COGNITIVE PERFORMANCE ON THE PHONETIC FLUENCY TEST EFFECT OF TACTILE STIMULI ON LOCOMOTOR RHYTHM UNDERGRADUATE RESEARCH PIPELINE IN MATHEMATICS COLLEGE OF SAINT MARY ELEMENTARY SCIENCE OUTREACH PROGRAM FOSTERING STUDENT AWARENESS ON GLOBAL CLIMATE CHANGE AND ENVIRONMENTAL STEWARDSHIP THROUGH CURRICULAR AND CO-CURRICULAR ACTIVITIES AUTONOMOUS RC CAR HIGH-ALTITUDE BALLOON SOLAR PANEL VOLTAGE VARIATION MICROBENTHIC ALGAE DENSITIES IN THE DUPLIN WATERSHED ESTIMATING UNCERTAINTY OF REFLECTANCE AND ERROR PROPAGATION IN VEGETATION INDICES ESTIMATING SURFACE VISIBILITY ON THE U.S. EAST COAST: INCORPORATING THE AEROSOL VERTICAL PROFILE FROM GEOS-5 EFFECTS OF VOLCANIC EMISSIONS ON THE EARTH-ATMOSPHERE SYSTEM OBSERVING THE TRANSPORTATION OF DUST ON EARTH USING MISR ARGOS AND MICROGRAVITY FREE FLYER EVALUATION UNL LUNABOTICS TEAM: DESIGNING A ROBOT FOR THE NASA LUNABOTICS ROBOT COMPETITION DESIGN, BUILD, FLY UNIVERSITY STUDENT LAUNCH INITIATIVE EHD THIN FILM BOILING IN MICROGRAVITY ENVIRONMENTS COMBINING SATELLITE OBSERVATIONS OF FIRE ACTIVITY AND NUMERICAL WEATHER PREDICTION TO IMPROVE THE PREDICTION OF SMOKE EMISSIONS SEARCH FOR ASYMMETRIC INTERACTIONS BETWEEN CHIRAL MOLECULES AND SPIN-POLARIZED ELECTRONS AUTOIGNITION IN AN UNSTRAINED METHANOL/AIR MIXING LAYER ANALYSIS OF THE HST/COS SPECTRUM OF THE MASS OUTFLOW IN SEYFERT 1 GALAXY MRK 279 CHARACTERIZATION OF A 5.8KV SIC PIN DIODE FOR ELECTRIC SPACE PROPULSION APPLICATIONS WIRELESS POWER TRANSFER: DESIGN AND APPLICATION FORCE SENSING OF GRASPING EVENTS FOR MINIATURE SURGICAL ROBOTS UNDERSTANDING WALKING AND BREATHING COUPLING WHEN ABNORMAL BREATHING PATTERNS ARE PRESENT EXAMINING THE QUALITY OF MODIS REFLECTANCE PRODUCTS USING A FOUR-BAND SPECTRORADIOMETER INVESTIGATING LAND AND ATMOSPHERE CHARACTERISTICS DURING THE 2012 CENTRAL PLAINS DROUGHT USING MODIS AND TRMM PRODUCTS A MARXIST APPROACH TO US HISTORICAL ARCHAEOLOGY: A REVIEW AND SUMMARY OF THE HISTORY AND APPLICATION OF MARXISM ON THE FIELD OF HISTORICAL ARCHAEOLOGY IN THE US JOHN COLLIER, ANTHROPOLOGY, AND THE INDIAN NEW DEA

Proceedings: Aeronautics and Space Science

VARIABILITY IN AGN ABSORPTION LINES BASED ON HUBBLE SPACE TELESCOPE/COS DATA BALQSO KINETIC LUMINOSITY DETERMINATION WITH C III* MEASUREMENTS BREWSTER ANGLE MICROSCOPY AND CHARACTERIZATIONS OF LANGMUIR FILMS SORTING LIGHT’S TOTAL ANGULAR MOMENTUM FOR COMMUNICATION SYSTEMS THE PHOSPHORYLATION PATTERN OF RPA2, IN RESPONSE TO DOUBLE-STRAND BREAKS, DIFFERS DEPENDING ON THE LOCATION IN THE CELL AND THE PHASE OF THE CELL CYCLE THE DIOPHANTINE EQUATION Ax^4+By^4=Cz^4 IN QUADRATIC FIELDS THE SBML STANDARD TO SHARE COMPUTATIONAL MODELS OF BIOLOGICAL SYSTEMS HIGH SPEED ELECTRO-DISCHARGE DRILLING AND WIRE ELECTRODE-DISCHARGE MACHINING OF TITANIUM ALLOYS FOR AEROSPACE APPLICATIONS ROUTING OVER THE INTERPLANETARY INTERNET WIRELESS INTEGRATED RELAY SYSTEM (WIRS) HUMAN REACTIONS TO FLUCTUATING NOISE CONDITIONS AS PRODUCED BY LOW-BOOM SUPERSONIC AIRCRAFT NONINVASIVE, AMBULATORY, LONG-TERM, DEEP GASTROINTESTINAL BIOSENSOR AND IMPLANTER RECONFIGURATION PLANNING OF MODULAR ROBOT UNDER UNCERTAINTY DYNAMIC GAIT ADAPTION IN FIXED CONFIGURATION FOR MODULAR SELF-RECONFIGURABLE ROBOTS USING FUZZY LOGIC CONTROL EARLY STAGE DEVELOPMENT OF A MEDICAL DEVICE FOR NON-INVASIVE MEASUREMENT OF INTRACRANIAL PRESSURE COMPLIANT LAPAROSCOPIC SURGICAL GRASPER MODULAR JOYSTICK FOR VIRTUAL REALITY SURGICAL SIMULATION NOVEL ASSISTIVE LOCOMOTOR TOOL FOR GAIT REHABILITATION IN THE ELDERLY GAIT VARIABILITY HAS NO RELATION TO COGNITIVE PERFORMANCE ON THE PHONETIC FLUENCY TEST EFFECT OF TACTILE STIMULI ON LOCOMOTOR RHYTHM UNDERGRADUATE RESEARCH PIPELINE IN MATHEMATICS COLLEGE OF SAINT MARY ELEMENTARY SCIENCE OUTREACH PROGRAM FOSTERING STUDENT AWARENESS ON GLOBAL CLIMATE CHANGE AND ENVIRONMENTAL STEWARDSHIP THROUGH CURRICULAR AND CO-CURRICULAR ACTIVITIES AUTONOMOUS RC CAR HIGH-ALTITUDE BALLOON SOLAR PANEL VOLTAGE VARIATION MICROBENTHIC ALGAE DENSITIES IN THE DUPLIN WATERSHED ESTIMATING UNCERTAINTY OF REFLECTANCE AND ERROR PROPAGATION IN VEGETATION INDICES ESTIMATING SURFACE VISIBILITY ON THE U.S. EAST COAST: INCORPORATING THE AEROSOL VERTICAL PROFILE FROM GEOS-5 EFFECTS OF VOLCANIC EMISSIONS ON THE EARTH-ATMOSPHERE SYSTEM OBSERVING THE TRANSPORTATION OF DUST ON EARTH USING MISR ARGOS AND MICROGRAVITY FREE FLYER EVALUATION UNL LUNABOTICS TEAM: DESIGNING A ROBOT FOR THE NASA LUNABOTICS ROBOT COMPETITION DESIGN, BUILD, FLY UNIVERSITY STUDENT LAUNCH INITIATIVE EHD THIN FILM BOILING IN MICROGRAVITY ENVIRONMENTS COMBINING SATELLITE OBSERVATIONS OF FIRE ACTIVITY AND NUMERICAL WEATHER PREDICTION TO IMPROVE THE PREDICTION OF SMOKE EMISSIONS SEARCH FOR ASYMMETRIC INTERACTIONS BETWEEN CHIRAL MOLECULES AND SPIN-POLARIZED ELECTRONS AUTOIGNITION IN AN UNSTRAINED METHANOL/AIR MIXING LAYER ANALYSIS OF THE HST/COS SPECTRUM OF THE MASS OUTFLOW IN SEYFERT 1 GALAXY MRK 279 CHARACTERIZATION OF A 5.8KV SIC PIN DIODE FOR ELECTRIC SPACE PROPULSION APPLICATIONS WIRELESS POWER TRANSFER: DESIGN AND APPLICATION FORCE SENSING OF GRASPING EVENTS FOR MINIATURE SURGICAL ROBOTS UNDERSTANDING WALKING AND BREATHING COUPLING WHEN ABNORMAL BREATHING PATTERNS ARE PRESENT EXAMINING THE QUALITY OF MODIS REFLECTANCE PRODUCTS USING A FOUR-BAND SPECTRORADIOMETER INVESTIGATING LAND AND ATMOSPHERE CHARACTERISTICS DURING THE 2012 CENTRAL PLAINS DROUGHT USING MODIS AND TRMM PRODUCTS A MARXIST APPROACH TO US HISTORICAL ARCHAEOLOGY: A REVIEW AND SUMMARY OF THE HISTORY AND APPLICATION OF MARXISM ON THE FIELD OF HISTORICAL ARCHAEOLOGY IN THE US JOHN COLLIER, ANTHROPOLOGY, AND THE INDIAN NEW DEA

Exhibiting Sha[2] on hyperelliptic jacobians

We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves, with an emphasis on the theory and practice of visualisation. Especially for hyperelliptic curves, this often enables the computation of ranks of Jacobians, even when the 2-Selmer bound does not bound the rank sharply. This was previously only possible for a few special cases. For curves of genus 2, we also demonstrate a connection with degree 4 del Pezzo surfaces, and show how the Brauer-Manin obstruction on these surfaces can be used to compute members of the Shafarevich-Tate group of Jacobians. We derive an explicit parametrised infinite family of genus 2 curves whose Jacobians have nontrivial members of the Sharevich-Tate group. Finally we prove that under certain conditions, the visualisation dimension for order 2 cocycles of Jacobians of certain genus 2 curves is 4 rather than the general bound of 32

Molecular Formula Identification using High Resolution Mass Spectrometry: Algorithms and Applications in Metabolomics and Proteomics

Wir untersuchen mehrere theoretische und praktische Aspekte der Identifikation der Summenformel von Biomolekülen mit Hilfe von hochauflösender Massenspektrometrie. Durch die letzten Forschritte in der Instrumentation ist die Massenspektrometrie (MS) zur einen der Schlüsseltechnologien für die Analyse von Biomolekülen in der Proteomik und Metabolomik geworden. Sie misst die Massen der Moleküle in der Probe mit hoher Genauigkeit, und ist für die Messdatenerfassung im Hochdurchsatz gut geeignet. Eine der Kernaufgaben in der MS-basierten Proteomik und Metabolomik ist die Identifikation der Moleküle in der Probe. In der Metabolomik unterliegen Metaboliten der Strukturaufklärung, beginnend bei der Summenformel eines Moleküls, d.h. der Anzahl der Atome jedes Elements. Dies ist der entscheidende Schritt in der Identifikation eines unbekannten Metabolits, da die festgelegte Formel die Anzahl der möglichen Molekülstrukturen auf eine viel kleinere Menge reduziert, die mit Methoden der automatischen Strukturaufklärung weiter analysiert werden kann. Nach der Vorverarbeitung ist die Ausgabe eines Massenspektrometers eine Liste von Peaks, die den Molekülmassen und deren Intensitäten, d.h. der Anzahl der Moleküle mit einer bestimmten Masse, entspricht. Im Prinzip können die Summenformel kleiner Moleküle nur mit präzisen Massen identifiziert werden. Allerdings wurde festgestellt, dass aufgrund der hohen Anzahl der chemisch legitimer Formeln in oberen Massenbereich eine exzellente Massengenaugkeit alleine für die Identifikation nicht genügt. Hochauflösende MS erlaubt die Bestimmung der Molekülmassen und Intensitäten mit hervorragender Genauigkeit. In dieser Arbeit entwickeln wir mehrere Algorithmen und Anwendungen, die diese Information zur Identifikation der Summenformel der Biomolekülen anwenden

The quantum measurement problem and physical reality: a computation theoretic perspective

Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not ruled out. On the other hand, empirical evidence suggests that NP-complete problems are intractable in the physical world. Likewise, computational problems known to be algorithmically uncomputable do not seem to be computable by any physical means. We suggest that this close correspondence between the efficiency and power of abstract algorithms on the one hand, and physical computers on the other, finds a natural explanation if the universe is assumed to be algorithmic; that is, that physical reality is the product of discrete sub-physical information processing equivalent to the actions of a probabilistic Turing machine. This assumption can be reconciled with the observed exponentiality of quantum systems at microscopic scales, and the consequent possibility of implementing Shor's quantum polynomial time algorithm at that scale, provided the degree of superposition is intrinsically, finitely upper-bounded. If this bound is associated with the quantum-classical divide (the Heisenberg cut), a natural resolution to the quantum measurement problem arises. From this viewpoint, macroscopic classicality is an evidence that the universe is in BPP, and both questions raised above receive affirmative answers. A recently proposed computational model of quantum measurement, which relates the Heisenberg cut to the discreteness of Hilbert space, is briefly discussed. A connection to quantum gravity is noted. Our results are compatible with the philosophy that mathematical truths are independent of the laws of physics.Comment: Talk presented at "Quantum Computing: Back Action 2006", IIT Kanpur, India, March 200

NCUWM Poster Abstracts 2010

Twelfth Annual Nebraska Conference for Undergraduate Women in Mathematics Poster Abstracts January 29-31, 2010 Holly Arrowood, Furman University Kristen Bretney, Loyola Marymount University Suzanne Carter, University of Iowa Nicole Casella, Ithaca College Morgan Chatham, University of Montevallo Lilith Ciccarelli, Bellarmine University Amber Clinton, Clarkson University Jalonda Coats, Tougaloo College Natalie Coston, Northern Arizona University Belinda Cruz, University of Texas Pan American Anita Doerfler, Northern Arizona University Clarice Dziak, Clarkson University Terra Fox, Hope College Samantha Fuller, Penn State University April Harry, Xavier University of Louisiana Anne Ho, Regis University Rachel Keyser, Bellarmine University Hannah Kolb, Illinois Institute of Technology Lauren Kraus, Wheaton College Amanda Kriesel, Minnesota State University - Mankato Florida Levidiotis, University of Mississippi Emese Lipcsey-Magyar, Skidmore College Melissa Martinez, University of Puerto Rico at Cayey Laura McCormick, Louisiana St. University - Shreveport Brittney Miller, University of Southern California Krista Newell, University of Wisconsin - Oshkosh Catie Patterson, Furman University Katherine Poulsen, Columbia University Stephanie Reed, University of South Dakota Lauren Schmidt, Murray State University Emily Sergel, Rutgers University Ngoc Thai, Truman State University Jasmin Uribe, University of Arizona Kan Wu, Purdue University - Calumet Guangtao Zhang, Clarkson University Jingyu Zhao, Stony Brook Universit