A new proof for the decidability of D0L ultimate periodicity

We give a new proof for the decidability of the D0L ultimate periodicity problem based on the decidability of p-periodicity of morphic words adapted to the approach of Harju and Linna.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Buyback Problem - Approximate matroid intersection with cancellation costs

In the buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to some constraints on the set of accepted bids. Decisions to reject bids are irrevocable, whereas decisions to accept bids may be canceled at a cost that is a fixed fraction of the bid value. Previous to our work, deterministic and randomized algorithms were known when the constraint is a matroid constraint. We extend this and give a deterministic algorithm for the case when the constraint is an intersection of $k$ matroid constraints. We further prove a matching lower bound on the competitive ratio for this problem and extend our results to arbitrary downward closed set systems. This problem has applications to banner advertisement, semi-streaming, routing, load balancing and other problems where preemption or cancellation of previous allocations is allowed

On the equation xk=z1k1z2k2⋯znkn in a free semigroup

AbstractWord equations of the form xk=z1k1z2k2⋯znkn are considered in this paper. In particular, we investigate the case where x is of different length than zi, for any i, and k and ki are at least 3, for all 1⩽i⩽n, and n⩽k. We prove that for those equations all solutions are of rank 1, that is, x and zi are powers of the same word for all 1⩽i⩽n. It is also shown that this result implies a well-known result by Appel and Djorup about the more special case where ki=kj for all 1⩽i<j⩽n

The Identity Correspondence Problem and its Applications

In this paper we study several closely related fundamental problems for words and matrices. First, we introduce the Identity Correspondence Problem (ICP): whether a finite set of pairs of words (over a group alphabet) can generate an identity pair by a sequence of concatenations. We prove that ICP is undecidable by a reduction of Post's Correspondence Problem via several new encoding techniques. In the second part of the paper we use ICP to answer a long standing open problem concerning matrix semigroups: "Is it decidable for a finitely generated semigroup S of square integral matrices whether or not the identity matrix belongs to S?". We show that the problem is undecidable starting from dimension four even when the number of matrices in the generator is 48. From this fact, we can immediately derive that the fundamental problem of whether a finite set of matrices generates a group is also undecidable. We also answer several question for matrices over different number fields. Apart from the application to matrix problems, we believe that the Identity Correspondence Problem will also be useful in identifying new areas of undecidable problems in abstract algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the published journal version of this article, see footnote 3 on page 1

Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Statin Adherence, Utilisation, and Prescribing Patterns. Improving effectiveness of treatment

Statins are one of the most widely studied and evidence-based medications. Randomised controlled trials have provided convincing evidence on the benefits of statin therapy in preventing cardiovascular events. Despite proven benefits, low costs, and few adverse effects, everyday effectiveness of statins is limited, since adherence to statin therapy is poor. This thesis was conducted as four pharmacoepidemiological studies using register data on statin users in real clinical care. The main purpose of the study was to evaluate prescribing patterns and to discover the lifestyle factors predicting statin nonadherence and discontinuation. This knowledge is essential in order to help physicians to motivate the adherence of their patients to treatment. In Finland, from 1998 to 2004, the number of statin initiators nearly doubled. The discovered channelling of atorvastatin and simvastatin may have affected the treatment outcomes at the public health level. It is possible that money spent on statins in Finland in 1998‒2004 could have been used in a more cost-effective way. In 2015, the percentage of patients receiving reimbursement for statins was 12% of the total population. Thus, it is a major public health and economic challenge to improve statin effectiveness and allocate therapy correctly. Among the participants with cardiovascular comorbidities, risky alcohol use or clustering of lifestyle risks were predictors of nonadherence. In addition, the prevalence of nonadherence to statins increased after retirement among both men and women. This increase in post-retirement nonadherence was highest among those receiving statins for secondary prevention. Discontinuation of statin therapy was predicted by high patient co-payment, and in women, by risky alcohol use. Recognising the predictors of nonadherence to statins is important because nonadherence is associated with an increased risk of adverse cardiovascular outcomes and higher healthcare costs. In conclusion, optimal outcomes in medical therapy require both efficacious medications and adherence to those treatments. When prescribing statins to eligible patients, the physician’s clinical expertise in recognising patients at risk of statin discontinuation and nonadherence, as well as their ability to increase adherence, may have a great effect on public health.Statiinihoitoon sitoutuminen, lääkekäyttö ja -määräykset. Hoidon vaikuttavuutta parantamassa. Kattavasti tutkittu ja näyttöön perustuva statiinilääkitys on oleellinen osa sydän- ja verisuonitautien ehkäisyä ja hoitoa. Satunnaistetuissa, kontrolloiduissa hoitotutkimuksissa osoitetusta tehosta, matalasta kustannuksesta ja vähäisistä haittavaikutuksista huolimatta statiinien vaikuttavuus arkielämässä jää odotettua heikommaksi, mikäli hoitoon sitoudutaan huonosti. Tämä väitöskirja koostuu neljästä lääke-epidemiologisesta tutkimuksesta, joissa arkielämän statiinikäyttöä tutkittiin rekisteritiedon avulla. Tutkimuksen tavoitteena oli sekä selvittää statiinien käyttöä ja lääkemääräyskäytäntöjä että tunnistaa hoitoon sitoutumiseen vaikuttavia tekijöitä, jotta käytännön lääkärit voisivat lääkehoidon toteutumisen seurannassa paremmin ylläpitää potilaan hoitomotivaatiota. Statiinilääkityksen aloittajien määrä lähes kaksinkertaistui Suomessa vuodesta 1998 vuoteen 2004. Tässä tutkimuksessa havaittu atorva- ja simvastatiinin kanavoituminen viittaa siihen, että statiineihin sijoitettu raha olisi mahdollisesti voitu Suomessa vuosina 1998–2004 käyttää kustannustehokkaammin. Vuonna 2015 statiineista sai sairausvakuutuskorvausta lähes joka kahdeksas suomalainen, minkä vuoksi statiinihoidon oikea kohdentaminen ja vaikuttavuuden parantaminen ovat merkittäviä sekä kansanterveyden että -talouden kannalta. Tämä tutkimus osoittaa, että haitallinen alkoholin käyttö ja elämäntapariskien kasautuminen ennustivat huonoa statiinihoitoon sitoutumista niillä tutkittavilla, joilla oli aiemmin diagnosoitu sydän- ja verisuonitauti tai diabetes. Myös eläköityminen lisäsi huonosti statiinihoitoon sitoutuneiden osuutta sekä miesten että naisten joukossa. Vaikutus tuli selvimmin esiin sekundaaripreventiopotilailla. Statiinihoidon aloittaneista 12 % lopetti lääkityksen ensimmäisen vuoden aikana. Hoidon ennenaikaista lopettamista ennusti korkeampi potilaan maksama osuus lääkekustannuksesta, naisilla myös haitallinen alkoholin käyttö. Edellä mainittujen tekijöiden tunnistaminen on tärkeää, sillä huonon hoitoon sitoutumisen tai hoidon ennenaikaisen lopettamisen tiedetään lisäävän haitallisia valtimosairaustapahtumia ja terveydenhuollon kokonaiskustannuksia. Järkevän ja ihanteellisesti vaikuttavan lääkehoidon edellytyksenä on sopivan käyttöaiheen ja sopivan lääkkeen valinnan lisäksi se, että potilas ymmärtää lääkityksensä merkityksen ja sitoutuu hoitoon. Lääkehoidon lopettamiseen tai hoitoon sitoutumattomuuteen liittyvien riskien tunnistaminen voi merkittävästi edistää kansanterveyttä.Siirretty Doriast

On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

On the steps of Emil Post : from normal systems to the correspondence decision problem

In 1946, Emil Leon Post (Bulletin of Amer. Math. Soc. 52 (1946), 264-268) introduced his famouscorrespondence decision problem, nowadays known as the Post Correspondence Problem (PCP).Post proved the undecidability of the PCP by areduction from his normal systems. In the presentarticle we follow the steps of Post, and give another, somewhat simpler and more straightforwardproof of the undecidability of the problem by using the same source of reductions as Post did.We investigate these, very different, techniques, and point out out some peculiarities in theapproach used by Post