Construction Of A Rich Word Containing Given Two Factors

A finite word $w$ with $\vert w\vert=n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is attained, the word $w$ is called \emph{rich}. Let \Factor(w) be the set of factors of the word $w$. It is known that there are pairs of rich words that cannot be factors of a common rich word. However it is an open question how to decide for a given pair of rich words $u,v$ if there is a rich word $w$ such that \{u,v\}\subseteq \Factor(w). We present a response to this open question:\\ If $w_1, w_2,w$ are rich words, $m=\max{\{\vert w_1\vert,\vert w_2\vert\}}$, and \{w_1,w_2\}\subseteq \Factor(w) then there exists also a rich word $\bar w$ such that \{w_1,w_2\}\subseteq \Factor(\bar w) and $\vert \bar w\vert\leq m2^{k(m)+2}$, where $k(m)=(q+1)m^2(4q^{10}m)^{\log_2{m}}$ and $q$ is the size of the alphabet. Hence it is enough to check all rich words of length equal or lower to $m2^{k(m)+2}$ in order to decide if there is a rich word containing factors $w_1,w_2$

Repetitions in infinite palindrome-rich words

Rich words are characterized by containing the maximum possible number of distinct palindromes. Several characteristic properties of rich words have been studied; yet the analysis of repetitions in rich words still involves some interesting open problems. We address lower bounds on the repetition threshold of infinite rich words over 2 and 3-letter alphabets, and construct a candidate infinite rich word over the alphabet $\Sigma_2=\{0,1\}$ with a small critical exponent of $2+\sqrt{2}/2$. This represents the first progress on an open problem of Vesti from 2017.Comment: 12 page

Impact of electronic reminders on venous thromboprophylaxis after admissions and transfers

Objective Clinical decision support has the potential to improve prevention of venous thromboembolism (VTE). The purpose of this prospective study was to analyze the effect of electronic reminders on thromboprophylaxis rates in wards to which patients were admitted and transferred. The latter was of particular interest since patient handoffs are considered to be critical safety issues. Methods The trial involved two study periods in the six departments of a university hospital, three of which were randomly assigned to the intervention group displaying reminders during the second period. At 6 h after admission or transfer, the algorithm checked for prophylaxis orders within 0-30 h of the patient's arrival, increasing the specificity of the displayed reminders. Results The significant impact of the reminders could be seen by prophylaxis orders placed 6-24 h after admission (increasing from 8.6% (223/2579) to 12% (307/2555); p<0.0001) and transfer (increasing from 2.4% (39/1616) to 3.7% (63/1682); p=0.034). In admission wards, the rate of thromboprophylaxis increased from 62.4% to 67.7% (p<0.0001), and in transfer wards it increased from 80.2% to 84.3% (p=0.0022). Overall, the rate of prophylaxis significantly increased in the intervention group from 69.2% to 74.3% (p<0.0001). No significant changes were observed in the control group. Postponing prophylaxis checks to 6 h after admissions and transfers reduced the number of reminders by 62% and thereby minimized the risk of alert fatigue. Conclusions The reminders improved awareness of VTE prevention in both admission and transfer wards. This approach may contribute to better quality of care and safer patient handoff

On Kaluza's sign criterion for reciprocal power series

T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzy\.z is applied.Comment: 13 page

Case report: bilateral Mooren ulcer in association with hepatitis C

Background: Mooren ulcer has been considered as an idiopathic autoimmune keratitis. However, it has been in some cases suggested to be associated with hepatitis C, although the evidence is very vague.Case presentation: We present a case of a man who was diagnosed with a primary Mooren ulcer in his right eye. The eye became blind despite of intensive treatment with local medications and extensive surgical procedures. After 10 years, the patient was diagnosed with the same disease, now in his left, previously healthy eye. There was no history that would suggest a secondary Mooren ulcer, but a chronic hepatitis C infection was detected. Treatment was targeted against hepatitis C (ribavirin and interferon) in addition to immunosuppressive medical and surgical treatment which resulted in a full and more than 6 years lasting remission of the disease.Conclusions: Whether the immunomodulatory and immunosuppressive medication against hepatitis C was the key reason for the good results in the treatment of the second eye, remains elusive. The causality of hepatitis C with respect to the pathogenesis of Mooren ulcer on this patient remains open, but should be considered as one of the possible etiological factors of the disease

On Words with the Zero Palindromic Defect

We study the set of finite words with zero palindromic defect, i.e., words rich in palindromes. This set is factorial, but not recurrent. We focus on description of pairs of rich words which cannot occur simultaneously as factors of a longer rich word

Is post-trabeculectomy hypotony a risk factor for subsequent failure? A case control study

BACKGROUND: Ocular hypotony results in an increased break down of the blood-aqueous barrier and an increase in inflammatory mediator release. We postulate that this release may lead to an increased risk of trabeculectomy failure through increased bleb scarring. This study was designed to try to address the question if hypotony within one month of trabeculectomy for Primary Open Angle Glaucoma (POAG), is a risk factor for future failure of the filter. METHODS: We performed a retrospective, case notes review, of patients who underwent trabeculectomy for POAG between Jan 1995 and Jan 1996 at our hospital. We identified those with postoperative hypotony within 1 month of surgery. Hypotony was defined as an intraocular pressure (IOP) < 8 mmHg or an IOP of less than 10 mmHg with choroidal detachment or a shallow anterior chamber. We compared the survival times of the surgery in this group with a control group (who did not suffer hypotony as described above), over a 5 year period. Failure of trabeculectomy was defined as IOP > 21 mmHg, or commencement of topical antihypertensives or repeat surgery. RESULTS: 97 cases matched our inclusion criteria, of these 38 (39%) experienced hypotony within 1 month of surgery. We compared the survival times in those patients who developed hypotony with those who did not using the log-rank test. This data provided evidence of a difference (P = 0.0492) with patients in the hypotony group failing more rapidly than the control group. CONCLUSION: Early post-trabeculectomy hypotony (within 1 month) is associated with reduced survival time of blebs

A low-carbohydrate diet may prevent end-stage renal failure in type 2 diabetes. A case report

An obese patient with type 2 diabetes whose diet was changed from the recommended high-carbohydrate, low-fat type to a low-carbohydrate diet showed a significant reduction in bodyweight, improved glycemic control and a reversal of a six year long decline of renal function. The reversal of the renal function was likely caused by both improved glycemic control and elimination of the patient's obesity. Insulin treatment in type 2 diabetes patients usually leads to weight increase which may cause further injury to the kidney. Although other unknown metabolic mechanisms cannot be excluded, it is likely that the obesity caused by the combination of high-carbohydrate diet and insulin in this case contributed to the patient's deteriorating kidney function. In such patients, where control of bodyweight and hyperglycemia is vital, a trial with a low-carbohydrate diet may be appropriate to avoid the risk of adding obesity-associated renal failure to already failing kidneys