Algebraic Independence and Blackbox Identity Testing

Algebraic independence is an advanced notion in commutative algebra that generalizes independence of linear polynomials to higher degree. Polynomials {f_1, ..., f_m} \subset \F[x_1, ..., x_n] are called algebraically independent if there is no non-zero polynomial F such that F(f_1, ..., f_m) = 0. The transcendence degree, trdeg{f_1, ..., f_m}, is the maximal number r of algebraically independent polynomials in the set. In this paper we design blackbox and efficient linear maps \phi that reduce the number of variables from n to r but maintain trdeg{\phi(f_i)}_i = r, assuming f_i's sparse and small r. We apply these fundamental maps to solve several cases of blackbox identity testing: (1) Given a polynomial-degree circuit C and sparse polynomials f_1, ..., f_m with trdeg r, we can test blackbox D := C(f_1, ..., f_m) for zeroness in poly(size(D))^r time. (2) Define a spsp_\delta(k,s,n) circuit C to be of the form \sum_{i=1}^k \prod_{j=1}^s f_{i,j}, where f_{i,j} are sparse n-variate polynomials of degree at most \delta. For k = 2 we give a poly(sn\delta)^{\delta^2} time blackbox identity test. (3) For a general depth-4 circuit we define a notion of rank. Assuming there is a rank bound R for minimal simple spsp_\delta(k,s,n) identities, we give a poly(snR\delta)^{Rk\delta^2} time blackbox identity test for spsp_\delta(k,s,n) circuits. This partially generalizes the state of the art of depth-3 to depth-4 circuits. The notion of trdeg works best with large or zero characteristic, but we also give versions of our results for arbitrary fields.Comment: 32 pages, preliminary versio

Optimierung der Operationstechnik bei Cochlea-Implantat-Versorgung zur Verringerung von intracochleären Druckveränderungen

Einführung Der Erhalt des Restgehörs und die Verringerung von intracochleären Schäden sind zwei der wichtigsten Grundsätze in der modernen Cochlea-Implantat-Chirurgie. Intracochleäre Druckveränderungen haben Einfluss auf den Erhalt des Restgehörs und sollten mithin so gering wie möglich gehalten werden. Die präsentierten Arbeiten befassen sich mit den Veränderungen intracochleärer Drücke während der Insertion einer Cochlea-Implantat-Elektrode und dem Einfluss verschiedener Konditionen auf intracochleäre Druckveränderungen. Material und Methoden Die Messungen wurden jeweils an einem künstlichen Cochleamodell durchgeführt, wobei die intracochleären Druckveränderungen mit einem mikro-optischen Drucksensor in der Apex des Modells aufgezeichnet wurden. Die Insertionen der Cochlea-Implantat-Elektroden wurden ein-Punkt-gestützt oder zwei-Punkt-gestützt durchgeführt. Bei den Messungen wurde teilweise eine Elektrode verwendet oder zwei Elektroden mit unterschiedlichen Eigenschaften. Für die Messungen der Rundfenstereröffnungen wurde das runde Fenster des artifiziellen Modells mit einer Polyethylenfolie abgedeckt und in mehreren unterschiedlichen Konditionen eröffnet. Ergebnisse Bei der ein-Punkt-gestützten Methode wird die Amplitude der intracochleären Druckveränderungen mit Zunahme der Insertionstiefe signifikant geringer. Bei dem Vergleich zweier unterschiedlicher CI-Elektroden zeigte sich, dass bei Verwendung der perimodiolären Nucleus Contour Advance™ Elektrode im Gegensatz zu der geraden Nucleus slim straight™ Elektrode, bei gleicher Insertionszeit, signifikant höhere intracochleäre Druckwerte und Amplituden auftraten. Signifikant geringere intracochleäre Druckschwankungen konnten bei der Eröffnung des RW mit dem Diodenlaser erzielt werden. Des Weiteren gab es signifikante Unterschiede bei der RW-Eröffnung unter feuchten und trockenen Bedingungen. Schlussfolgerung Es wird immer offensichtlicher, dass in der modernen CI-Chirurgie viele verschiedene Elemente Einfluss auf das funktionelle Ergebnis haben. Eines dieser Elemente ist die Minimierung intracochleärer Druckschwankungen, welche Einfluss auf den angestrebten Erhalt des Restgehörs haben. Intracochleäre Druckschwankungen treten bei der Insertion der Elektrode in die Cochlea sowie bei der Eröffnung des RW auf. Diese Schwankungen können einerseits durch die maximale Unterstützung der Hand des Operateurs, durch die Wahl der Technik bei der Eröffnung des RF als auch durch die Wahl der CI-Elektrode beeinflusst werden. Es sollte weiter untersucht werden, inwieweit die am Modell gemessenen Ergebnisse auf die in vivo Cochlea übertragbar sind.Abstract Introduction The preservation of residual hearing and the minimization of intracochlear trauma are two major goals in modern cochlear implant surgery. Intracochlear fluid pressure (ICFP) changes are assumed to have impact on the preservation of residual hearing and should therefore kept low. The presented studies are dealing with the behavior of ICFP changes during the implantion of cochlea implant electrodes and the choice of technique for the best approach opening the round window. Furthermore the studies deal with the influence of the selection of different kinds of cochlear implant electrodes. Material and methods All measurements were made in an artificial model of the human cochlear with the micro-optical pressure sensor placed in the apex of the model. The insertions of the cochlea implant electrodes were partially performed one-point-supported and partially two-points-supported. One part of the measurements was performed with a single cochlear implant electrode. In the other part of the other measurements two different electrode types were used. For the measurements of the opening of the round window membrane, the round window of the artificial model was covered with a polyethylene foil, which was opened under different conditions. Results Significant reductions were observed in terms of the amplitude variation, using the onepoint- supported insertion condition. By comparison of two different cochlear implant electrodes there were significantly higher ICFP changes and amplitude variations over the same insertion time using the perimodiolar Nucleus Contour Advance™ electrode than the straight Nucleus slim straight™ electrode. Relating to the RW opening, significantly lower ICFP changes could be achieved using the diode laser instead of the cannula. In addition we found significant lower pressure changes when opening the RW in a transfluid instead of dry condition. Conclusion Many elements have impact on modern CI surgery. One element is the minimization of ICFP changes, which have a stake in preservation of residual hearing. ICFP changes appear during the insertion of the cochlear implant electrode as well as during opening the RW. These pressure changes could be minimized by using maximum support of the surgeon's hand, careful RW opening and critical selection of the cochlear implant electrode array. It should be further investigated to what extend the taken measurements, using an artificial cochlear model, can be transferred to the human cochlear, to continuously improve modern CI surgery

Independence in Algebraic Complexity Theory

This thesis examines the concepts of linear and algebraic independence in algebraic complexity theory. Arithmetic circuits, computing multivariate polynomials over a field, form the framework of our complexity considerations. We are concerned with polynomial identity testing (PIT), the problem of deciding whether a given arithmetic circuit computes the zero polynomial. There are efficient randomized algorithms known for this problem, but as yet deterministic polynomial-time algorithms could be found only for restricted circuit classes. We are especially interested in blackbox algorithms, which do not inspect the given circuit, but solely evaluate it at some points. Known approaches to the PIT problem are based on the notions of linear independence and rank of vector subspaces of the polynomial ring. We generalize those methods to algebraic independence and transcendence degree of subalgebras of the polynomial ring. Thereby, we obtain efficient blackbox PIT algorithms for new circuit classes. The Jacobian criterion constitutes an efficient characterization for algebraic independence of polynomials. However, this criterion is valid only in characteristic zero. We deduce a novel Jacobian-like criterion for algebraic independence of polynomials over finite fields. We apply it to obtain another blackbox PIT algorithm and to improve the complexity of testing the algebraic independence of arithmetic circuits over finite fields.Die vorliegende Arbeit untersucht die Konzepte der linearen und algebraischen Unabhängigkeit innerhalb der algebraischen Komplexitätstheorie. Arithmetische Schaltkreise, die multivariate Polynome über einem Körper berechnen, bilden die Grundlage unserer Komplexitätsbetrachtungen. Wir befassen uns mit dem polynomial identity testing (PIT) Problem, bei dem entschieden werden soll ob ein gegebener Schaltkreis das Nullpolynom berechnet. Für dieses Problem sind effiziente randomisierte Algorithmen bekannt, aber deterministische Polynomialzeitalgorithmen konnten bisher nur für eingeschränkte Klassen von Schaltkreisen angegeben werden. Besonders von Interesse sind Blackbox-Algorithmen, welche den gegebenen Schaltkreis nicht inspizieren, sondern lediglich an Punkten auswerten. Bekannte Ansätze für das PIT Problem basieren auf den Begriffen der linearen Unabhängigkeit und des Rangs von Untervektorräumen des Polynomrings. Wir übertragen diese Methoden auf algebraische Unabhängigkeit und den Transzendenzgrad von Unteralgebren des Polynomrings. Dadurch erhalten wir effiziente Blackbox-PIT-Algorithmen für neue Klassen von Schaltkreisen. Eine effiziente Charakterisierung der algebraischen Unabhängigkeit von Polynomen ist durch das Jacobi-Kriterium gegeben. Dieses Kriterium ist jedoch nur in Charakteristik Null gültig. Wir leiten ein neues Jacobi-artiges Kriterium für die algebraische Unabhängigkeit von Polynomen über endlichen Körpern her. Dieses liefert einen weiteren Blackbox-PIT-Algorithmus und verbessert die Komplexität des Problems arithmetische Schaltkreise über endlichen Körpern auf algebraische Unabhängigkeit zu testen

A New Model-Free Sliding Mode Control Method with Estimation of Control Input Error

A new type of sliding mode controller scheme, which requires no knowledge of system model, is derived in this work. The controller is solely based on previous control inputs and state measurements to generate the updated control input effort. The only knowledge required to derive the controller is the system order and the bounds of the control input gain, if one exists. The switching gain, which is required to drive the system states onto the sliding surface in the presence of disturbances and uncertainties, is derived using Lyapunov’s stability theorem, ensuring closed-loop asymptotic stability. The chattering effect, which is excited by the switching gain due to high activity of the control input, is reduced by using a smoothing boundary layer into the control law form. Simulations are performed, using first and second-order, linear and nonlinear systems, to test the performance of the new control law. In the last part of this work, the problem with state measurement noise is addressed. Results of the simulations validates the feasibility of the proposed control scheme

TokenPasser: A petri net specification tool

In computer program design it is essential to know the effectiveness of different design options in improving performance, and dependability. This paper provides a description of a CAD tool for distributed hierarchical Petri nets. After a brief review of Petri nets, Petri net languages, and Petri net transducers, and descriptions of several current Petri net tools, the specifications and design of the TokenPasser tool are presented. TokenPasser is a tool to allow design of distributed hierarchical systems based on Petri nets. A case study for an intelligent robotic system is conducted, a coordination structure with one dispatcher controlling three coordinators is built to model a proposed robotic assembly system. The system is implemented using TokenPasser, and the results are analyzed to allow judgment of the tool

Straight spinning cosmic strings in Brans-Dicke gravity

It is presented an exact solution of straight spinning cosmic strings in Brans-Dicke theory of gravitation. The possibility of the existence of closed timelike curves around these cosmic strings is analyzed. Furthermore, the stability about the formation of the topological defect discussed here is checked. It is shown the existence of a suitable choice for the integration constants in which closed timelike curves are not allowed. We also verify if it is possible that the obtained spacetime can be the source that describes the observed rotational curves in some galaxies.Comment: 13 pages, 1 figur

Cooccurrences spécifiques et représentations graphiques, le nouveau " Thème " d'Hyperbase

International audienceFinding word cooccurrences and calculating the specificity scores is one of the most popular statistical methods in the analysis of textual data. Within Hyperbase, there is a " theme " feature for this purpose, which is capable of locating words that are used more commonly near a given word form, grammatical structure or lemma. The graphical representation of such an analysis is often challenging ; more than a list of the cooccurring words, it should be able to indicate the order, the score and the relations between pairs of words. Now that Hyperbase has a Web version, this article proposes a new approach for the " theme " feature : the calculation of cooccurrences has been extended to include the second level. The accompanying graphical representation is betting on new visual features in order to simplify reading the results and render the underlying calculation more explicit. Résumé Le calcul des cooccurrents spécifiques d'un mot est une des méthodes statistiques les plus populaires de l'ADT. Le logiciel Hyperbase a introduit cette notion avec la fonction " Th eme " qui rend compte du lexique surutilisé autour d'une forme, d'une structure grammaticale ou d'un lemme. La représentation graphique d'une telle analyse est souvent loin d'ˆ etré evidente. Plus que la simple liste des cooccurrents spécifiques , elle se doit de nous indiquer aussi l'ordre, l'´ ecart ainsi que les relations entre chaque paire de mots. Avec l' arrivée de la version Web d'Hyperbase, nous proposons aujourd'hui une nouvelle approche de cette fonction. Le calcul se voit pour l'occasion approfondi, lui permettant d'identifier la cooccurrence dedeuxì eme niveau. La représentation graphique, quant a elle, fait le pari de simplifier la lecture du résultat de cette analyse tout en explicitant plus précisément les calculs sous-jacents

A nearly cylindrically symmetric source in the Brans-Dicke gravity as the generator of the rotational curves of the galaxies

Observation shows that the velocities of stars grow by approximately 2 to 3 orders of magnitude when the distances from the centers of the galaxies are in the range of $0.5$ kpc to $82.3$ kpc, before they begin to tend to a constant value. Up to know, the reason for this behavior is still a matter for debate. In this work, we propose a model which adequately describes this unusual behavior using a (nearly) cylindrical symmetrical solution in the framework of a scalar-tensor-like (the Brans-Dicke model) theory of gravity.Comment: 24 pages, 4 figures, accepted for publication in Eur. Phys. J.