Breaking the PPSZ Barrier for Unique 3-SAT

The PPSZ algorithm by Paturi, Pudl\'ak, Saks, and Zane (FOCS 1998) is the fastest known algorithm for (Promise) Unique k-SAT. We give an improved algorithm with exponentially faster bounds for Unique 3-SAT. For uniquely satisfiable 3-CNF formulas, we do the following case distinction: We call a clause critical if exactly one literal is satisfied by the unique satisfying assignment. If a formula has many critical clauses, we observe that PPSZ by itself is already faster. If there are only few clauses allover, we use an algorithm by Wahlstr\"om (ESA 2005) that is faster than PPSZ in this case. Otherwise we have a formula with few critical and many non-critical clauses. Non-critical clauses have at least two literals satisfied; we show how to exploit this to improve PPSZ.Comment: 13 pages; major revision with simplified algorithm but slightly worse constant

Variable structure based control strategy for treatment of HCV infection

Hepatitis C is such a harmful disease which can lead to serious health problems and it is caused by the Hepatitis C Virus (HCV) which causes liver inflammation and sometimes liver cancer. In this work, the control treatment strategy for HCV infection has been proposed. The advanced nonlinear dynamical mathematical model of HCV that has two control inputs and three state variables such as virions, infected hepatocytes and uninfected hepatocytes are considered for controller design in this research work. Moreover, four nonlinear controllers such as the Fractional Order Terminal Sliding Mode Controller (FOTSMC), Integral Terminal Sliding Mode Controller (ITSMC), Double Integral Sliding Mode Controller (DISMC) and Integral Sliding Mode Controller (ISMC) have been proposed in this work for HCV infection control inside the human body. In order to control the amount of uninfected hepatocytes to its required maximum safe limit, controllers are designed for antiviral therapy in which the amount of virions and infected hepatocytes are tracked to zero. One control input is ribavirin which blocks virions production and the other is pegylated interferon (peg-IFN-a) that acts as reducing infected hepatocytes. By doing so, uninfected hepatocytes increase and achieve the required maximum safe limit. To prove the stability of the whole system, Lyapunov stability analysis is used in this work. Simulation results and comparative analysis are carried out by using MATLAB/Simulink. It can be depicted from the given results that the virions and infected hepatocytes are reduced to their required levels completely using FOTSMC and the Sustained Virologic Response (SVR) rate is also enhanced in it. It reduces the treatment period as compared to previous strategies introduced in the literature and also system behaves very nicely even in the presence of un-modeled disturbances

Variable Structure-Based Control for Dynamic Temperature Setpoint Regulation in Hospital Extreme Healthcare Zones

In critical healthcare units, such as operation theaters and intensive care units, healthcare workers require specific temperature environments at different stages of an operation, which depends upon the condition of the patient and the requirements of the surgical procedures. Therefore, the need for a dynamically controlled temperature environment and the availability of the required heating/cooling electric power is relatively more necessary for the provision of a better healthcare environment as compared to other commercial and residential buildings, where only comfortable room temperature is required. In order to establish a dynamic temperature zone, a setpoint regulator is required that can control the zone temperature with a fast dynamic response, little overshoot, and a low settling time. Thus, two zone temperature regulators have been proposed in this article, including double integral sliding mode control (DISMC) and integral terminal sliding mode control (ITSMC). A realistic scenario of a hospital operation theater is considered for evaluating their responses and performance to desired temperature setpoints. The performance analysis and superiority of the proposed controllers have been established by comparison with an already installed Johnson temperature controller (JTC) for various time spans and specific environmental conditions that require setpoints based on doctors’ and patients’ desires. The proposed controllers showed minimal overshoot and a fast settling response, making them ideal controllers for operation theater (OT) zone temperature control

Limit theorems and ergodicity for general bootstrap random walks

Given the increments of a simple symmetric random walk $(X_n)_{n\ge0}$, we characterize all possible ways of recycling these increments into a simple symmetric random walk $(Y_n)_{n\ge0}$ adapted to the filtration of $(X_n)_{n\ge0}$. We study the long term behavior of a suitably normalized two-dimensional process $((X_n,Y_n))_{n\ge0}$. In particular, we provide necessary and sufficient conditions for the process to converge to a two-dimensional Brownian motion (possibly degenerate). We also discuss cases in which the limit is not Gaussian. Finally, we provide a simple necessary and sufficient condition for the ergodicity of the recycling transformation, thus generalizing results from Dubins and Smorodinsky (1992) and Fujita (2008), and solving the discrete version of the open problem of the ergodicity of the general L\'evy transformation (see Mansuy and Yor, 2006).Comment: 22 pages, 2 figure

Evaluation of adverse drug reaction reports in adult patients on antiretroviral therepy in Ahmadu Bello University Teaching hospital Zaria-Nigeria

Antiretroviral therapy (ART) has reduced morbidity and mortality in HIV patients. In Nigeria, there are over 400,000 patients on ART in over 200 secondary and tertiary hospitals. However, data on adverse drug reactions (ADRs) due to ARTs are limited. The aim of this study was to evaluate ADRs reports in adult patients on ART in Ahmadu Bello University Teaching Hospital Zaria (ABUTH). The study was a retrospective cross-sectional study on randomly selected adult patients on ART with ADR reports in Nasara Clinic of ABUTH, between January, 2012 and December, 2013. Medical records and ADR reports of the patients were reviewed and fitted into a structured questionnaire. Data were analyzed using SPSS Version 20.0. The study reviewed the records of 302 patients on ART as per the sample size out of a total of 1405 patients in the register within the study period. Of the 302 patients, 109 (36.1%) were reported to have at least one form of ADR, majority of whom were females 65 (59.6%). The most common ADRs were cough (34%), skin rash (44%), headache (20%) and diarrhea (10%), with few cases of anemia (5.5%), lipodostrophy (3.6%) and neuropathy (1.8%). 55% and 98% had concomitant disease and medications respectively. The actions taken to manage the ADR were; specific treatment of the ADR (69.7%), change of ARV regimen (22%) and few cases of hospitalization (6.4%). In conclusion, the study revealed the occurrence of ADRs in adult patients on ART in ABUTH. These reactions occurred within few months of medication, and were found to be related to age, social factor, ART regimen, gender, as well as other concomitant diseases and medications. Close monitoring is required to prevent severe ADR and improve adherence.Keywords: Antiretroviral therapy, adverse drug reaction, cough, retrospectiv

Association Between Lipid Profile and Glyceamic Control in Sudanese Children with Type 1 Diabetes Mellitus at Gezira State, Sudan

Introduction: Diabetes mellitus describes a metabolic disorder of multiple aetiology characterized by chronic hyperglycemia with disturbances of carbohydrate, fat and protein metabolism resulting from defects in insulin secretion, insulin action, or both. Objectives This study aimed to assess the metabolic control of type 1 diabetes mellitus (T1DM) in Sudanese children. Methods: One hundred and seventy four children with type 1 diabetes mellitus were enrolled in this study; 56 healthy non-diabetic children served as a control group. Glycosylated hemoglobin (HbA1c), total cholesterol (TC), triacylglycerol (TG), low density lipoprotein-cholesterol (LDL-C), high density lipoprotein-cholesterol (HDL-C) were measured, very low density lipoprotein-cholesterol (VLDL), and LDL-C/HDL-C ratio were calculated. Results: HbA1c,TC, LDL-C LDL-C/HDL-C ratio and TG were significantly higher among diabetic group compared to non-diabetic group (P<0.001 and P<0.05 for TG).In the diabetic group, there was a positive significant correlation of: HbA1c with TC, TG, HDL- C, LDL-C, VLDL and LDL/HDL ratio; TC with TG, HDL- C, LDL-C, VLDL and LDL/HDL; TG with LDL- C, VLDL and LDL/HDL ratio; HDL-C with LDL-C;LDL-C with VLDL and LDL/ HDL;VLDL-C with LDL/HDL ratio. A significant negative correlation was observed between HDL- C and LDL/HDL ratio. Diabetic group with poor metabolic control (HbA1c level >8).had significantly higher levels of TC and LDL-C (P<0.001),TG and VLDL (P<0.01), HDL-C and LDL-C/ HDL-C ratio (P<0.05) compared with diabetic group with good metabolic control (HbA1c <8%). Conclusion: 85.63% of diabetic patients were found to have poor metabolic control (HbA1c level >8). يوصف مرض السكري بأنه من المسببات المرضية المتعددة التي تتميز بفرط  سكر الدم المزمن واضطراب في التمثيل الغذائي ( اضطرابات من الكربوهيدرات والدهون واستقلاب البروتين) الناتج عن نقص في إفراز الأنسولين، عمل الانسولين أو كليهما.هدفت هذه الدراسة لاستخدام التقييم الكيموحيوي لمعرفة مدي التحكم لضبط السكر عند مرضي السكري النوع الاول. إشتملت هذه الدراسه علي 174طفل مصابين مرض السكري و56 أصحاء من نفس العمر.تضمنت هذه الدراسة  القياسات الكيموحيويه الأتيه: خضاب الدم المسكر، الكوليستيرول ، ثلاثي أسيل الجليسرول و الكوليستيرول المرتبط  بالبروتينات الشحميه منخفضة وعاليه الكثافة والبروتينات الشحميه المنخفضة جدا ونسبة البروتينات الشحميه منخفضة الكثافة الي البروتينات الشحميه عالية الكثافة. وجد أن تركيز كل من خضاب الدم المسكر، الكوليستيرول ، الكوليستيرول المرتبط  بالبروتينات الشحميه منخفضة الكثافة ونسبة البروتينات الشحميه منخفضة الكثافة الي البروتينات الشحميه عالية الكثافة وثلاثي أسيل الجليسرول يرتفع إرتفاعا ذا معني عند مجموعة مرضي السكري.مستوي خضاب الدم المسكر يرتبط إرتباطا موجبا ذا معني مع كل من الكوليستيرول ، ثلاثي أسيل الجليسرول والبروتينات الشحميه عالية ومنخفضة الكثافة والبروتينات الشحميه المنخفضة جدا ونسبة البروتينات الشحميه منخفضة الكثافة الي البروتينات الشحميه عالية الكثافة، الكوليستيرول مع كل من ثلاثي أسيل الجليسرول والبروتينات الشحميه عالية و منخفضة الكثافة والبروتينات الشحميه المنخفضة جدا ونسبة البروتينات الشحميه منخفضة الكثافة الي البروتينات الشحميه عالية الكثافة ، يرتبط ثلاثي أسيل الجليسرول مع كل من البروتينات الشحميه منخفضة الكثافة والبروتينات الشحميه المنخفضة جدا ونسبة البروتينات الشحميه منخفضة الكثافة الي البروتينات الشحميه عالية الكثافة . كما أن  مستوي البروتينات الشحميه عالية الكثافة يرتبط إرتباطا ذا معني مع نسبة البروتينات الشحميه منخفضة الكثافة الي البروتينات الشحميه عالية الكثافة.طبقا لتقسيم مجموعة الدارسين لمرض السكري العالميه الأمريكيه أظهرت هذه الدراسه أن نسبة (85.63)  من المرضي يبلغ معدل خضاب الدم المسكر عندهم أكثر من  8% (ضبط غير مقبول) بينما  (%14.37) يبلغ معدل خضاب الدم المسكر عندهم أقل من  8% (ضبط مقبول).  وجدت هذه الدراسة ان مرضي السكري والذين لديهم ضبط غير مقبول لخضاب الدم المسكر ترتفع عندهم مستويات الكوليستيرول ، ثلاثي أسيل الجليسرول و الكوليستيرول المرتبط  بالبروتينات الشحميه منخفضة وعاليه الكثافة والبروتينات الشحميه المنخفضة جدا ونسبة البروتينات الشحميه منخفضة الكثافة الي البروتينات الشحميه عالية الكثافة ارتفاعا ذا معني مقارنة مرضي السكري والذين لديهم ضبط مقبول لخضاب الدم المسكر

Mitomycin C application in resistant caustic esophageal stricture

Background/purpose Caustic esophageal strictures still represent a catastrophic problem in children of our country. Management protocol is usually started by regular esophageal dilatation in which multiple sessions may be needed until the resolution of dysphagia; however, in many cases endoscopic dilatation fails and therefore esophageal replacement is eventually required. Our aim is to assess the role of mitomycin C application in the management of caustic esophageal stricture refractory to regular endoscopic dilatation.Patients and methods Patients with resistant caustic esophageal stricture were subjected to topical mitomycin C application on stricture site after endoscopic dilatation. Patients were followed up clinically using validated dysphagia score to assess the improvement of dysphagia, radiologically by contrast esophagogram and endoscopically to confirm resolution of the stricture. Results were analyzed and compared with results of a control group managed at the institution by a regular dilatation protocol.Results During the period January 2008 to June 2010, 12 patients with resistant caustic esophageal stricture were followed at our unit of whom six had a short esophageal stricture (< 3 cm) and six had a long stricture ( >3 cm). Topical mitomycin C application resulted in clinical and radiological resolution of dysphagia and strictures in 83% and 66% respectively, compared with 44 (eight out of 18 patients with short stricture) and 25% (two out of eight patients with long stricture) in the control group.Conclusion Mitomycin C application can markedly improve the outcome of patients with caustic esophageal stricture, reducing the number of required sessions for endoscopic dilatation. However, double-blinded randomized controlled trial is needed to prove its effectiveness.Keywords: caustic esophageal stricture, esophageal dilatation, mitomycin