13 research outputs found
Machine learning discovers invariants of braids and flat braids
We use machine learning to classify examples of braids (or flat braids) as
trivial or non-trivial. Our ML takes form of supervised learning using neural
networks (multilayer perceptrons). When they achieve good results in
classification, we are able to interpret their structure as mathematical
conjectures and then prove these conjectures as theorems. As a result, we find
new convenient invariants of braids, including a complete invariant of flat
braids.Comment: 24 page
Computing Data Distribution from Query Selectivities
We are given a set , where each
is a \emph{range} in , such as rectangle or ball, and denotes its \emph{selectivity}. The goal is to compute a small-size
\emph{discrete data distribution} , where and for each ,
and , such that is the most
\emph{consistent} with , i.e.,
is minimized. In a
database setting, corresponds to a workload of range queries over
some table, together with their observed selectivities (i.e., fraction of
tuples returned), and can be used as compact model for
approximating the data distribution within the table without accessing the
underlying contents.
In this paper, we obtain both upper and lower bounds for this problem. In
particular, we show that the problem of finding the best data distribution from
selectivity queries is -complete. On the positive side, we
describe a Monte Carlo algorithm that constructs, in time
, a discrete
distribution of size , such that
(for
) where the minimum is taken over all discrete distributions. We
also establish conditional lower bounds, which strongly indicate the
infeasibility of relative approximations as well as removal of the exponential
dependency on the dimension for additive approximations. This suggests that
significant improvements to our algorithm are unlikely
Computer Science 2019 APR Self-Study & Documents
UNM Computer Science APR self-study report and review team report for Spring 2019, fulfilling requirements of the Higher Learning Commission
SAT-based Analysis, (Re-)Configuration & Optimization in the Context of Automotive Product documentation
Es gibt einen steigenden Trend hin zu kundenindividueller Massenproduktion (mass customization), insbesondere im Bereich der Automobilkonfiguration. Kundenindividuelle Massenproduktion fĂŒhrt zu einem enormen Anstieg der KomplexitĂ€t. Es gibt Hunderte von Ausstattungsoptionen aus denen ein Kunde wĂ€hlen kann um sich sein persönliches Auto zusammenzustellen. Die Anzahl der unterschiedlichen konfigurierbaren Autos eines deutschen Premium-Herstellers liegt fĂŒr ein Fahrzeugmodell bei bis zu 10^80.
SAT-basierte Methoden haben sich zur Verifikation der StĂŒckliste (bill of materials) von Automobilkonfigurationen etabliert. Carsten Sinz hat Mitte der 90er im Bereich der SAT-basierten Verifikationsmethoden fĂŒr die Daimler AG Pionierarbeit geleistet. Darauf aufbauend wurde nach 2005 ein produktives Software System bei der Daimler AG installiert. SpĂ€ter folgten weitere deutsche Automobilhersteller und installierten ebenfalls SAT-basierte Systeme zur Verifikation ihrer StĂŒcklisten.
Die vorliegende Arbeit besteht aus zwei Hauptteilen. Der erste Teil beschĂ€ftigt sich mit der Entwicklung weiterer SAT-basierter Methoden fĂŒr Automobilkonfigurationen. Wir zeigen, dass sich SAT-basierte Methoden fĂŒr interaktive Automobilkonfiguration eignen. Wir behandeln unterschiedliche Aspekte der interaktiven Konfiguration. Darunter KonsistenzprĂŒfung, Generierung von Beispielen, ErklĂ€rungen und die Vermeidung von Fehlkonfigurationen. AuĂerdem entwickeln wir SAT-basierte Methoden zur Verifikation von dynamischen Zusammenbauten. Ein dynamischer Zusammenbau reprĂ€sentiert die chronologische Zusammenbau-Reihenfolge komplexer Teile.
Der zweite Teil beschĂ€ftigt sich mit der Optimierung von Automobilkonfigurationen. Wir erlĂ€utern und vergleichen unterschiedliche Optimierungsprobleme der Aussagenlogik sowie deren algorithmische LösungsansĂ€tze. Wir beschreiben AnwendungsfĂ€lle aus der Automobilkonfiguration und zeigen wie diese als aussagenlogisches Optimierungsproblem formalisiert werden können. Beispielsweise möchte man zu einer Menge an AusstattungswĂŒnschen ein Test-Fahrzeug mit minimaler ErgĂ€nzung weiterer Ausstattungen berechnen um Kosten zu sparen. DesWeiteren beschĂ€ftigen wir uns mit der Problemstellung eine kleinste Menge an Fahrzeugen zu berechnen um eine Testmenge abzudecken.
Im Rahmen dieser Arbeit haben wir einen Prototypen eines (Re-)Konfigurators, genannt AutoConfig, entwickelt. Unser (Re-)Konfigurator verwendet im Kern SAT-basierte Methoden und besitzt eine grafische BenutzeroberflĂ€che, welche interaktive Konfiguration erlaubt. AutoConfig kann mit Instanzen von drei groĂen deutschen Automobilherstellern umgehen, aber ist nicht alleine darauf beschrĂ€nkt. Mit Hilfe dieses Prototyps wollen wir die Anwendbarkeit unserer Methoden demonstrieren
Pseudo-contractions as Gentle Repairs
Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas
Assuming Data Integrity and Empirical Evidence to The Contrary
Background: Not all respondents to surveys apply their minds or understand
the posed questions, and as such provide answers which lack coherence, and
this threatens the integrity of the research. Casual inspection and limited
research of the 10-item Big Five Inventory (BFI-10), included in the dataset of
the World Values Survey (WVS), suggested that random responses may be
common.
Objective: To specify the percentage of cases in the BRI-10 which include
incoherent or contradictory responses and to test the extent to which the
removal of these cases will improve the quality of the dataset.
Method: The WVS data on the BFI-10, measuring the Big Five Personality (B5P), in South Africa (N=3 531), was used. Incoherent or contradictory responses were removed. Then the cases from the cleaned-up dataset were analysed for their theoretical validity.
Results: Only 1 612 (45.7%) cases were identified as not including incoherent
or contradictory responses. The cleaned-up data did not mirror the B5P- structure, as was envisaged. The test for common method bias was negative. Conclusion: In most cases the responses were incoherent. Cleaning up the data did not improve the psychometric properties of the BFI-10. This raises concerns about the quality of the WVS data, the BFI-10, and the universality of B5P-theory. Given these results, it would be unwise to use the BFI-10 in South Africa. Researchers are alerted to do a proper assessment of the
psychometric properties of instruments before they use it, particularly in a
cross-cultural setting
Leading Towards Voice and Innovation: The Role of Psychological Contract
Background: Empirical evidence generally suggests that psychological
contract breach (PCB) leads to negative outcomes. However, some literature
argues that, occasionally, PCB leads to positive outcomes.
Aim: To empirically determine when these positive outcomes occur, focusing
on the role of psychological contract (PC) and leadership style (LS), and
outcomes such as employ voice (EV) and innovative work behaviour (IWB).
Method: A cross-sectional survey design was adopted, using reputable
questionnaires on PC, PCB, EV, IWB, and leadership styles. Correlation
analyses were used to test direct links within the model, while regression
analyses were used to test for the moderation effects.
Results: Data with acceptable psychometric properties were collected from 11
organisations (N=620). The results revealed that PCB does not lead to
substantial changes in IWB. PCB correlated positively with prohibitive EV, but did not influence promotive EV, which was a significant driver of IWB. Leadership styles were weak predictors of EV and IWB, and LS only partially moderated the PCB-EV relationship. Conclusion: PCB did not lead to positive outcomes. Neither did LS influencing the relationships between PCB and EV or IWB. Further, LS only partially influenced the relationships between variables, and not in a manner which positively influence IWB