On Randomized Memoryless Algorithms for the Weighted kk-server Problem

The weighted $k$-server problem is a generalization of the $k$-server problem in which the cost of moving a server of weight $\beta_i$ through a distance $d$ is $\beta_i\cdot d$. The weighted server problem on uniform spaces models caching where caches have different write costs. We prove tight bounds on the performance of randomized memoryless algorithms for this problem on uniform metric spaces. We prove that there is an $\alpha_k$-competitive memoryless algorithm for this problem, where $\alpha_k=\alpha_{k-1}^2+3\alpha_{k-1}+1$; $\alpha_1=1$. On the other hand we also prove that no randomized memoryless algorithm can have competitive ratio better than $\alpha_k$. To prove the upper bound of $\alpha_k$ we develop a framework to bound from above the competitive ratio of any randomized memoryless algorithm for this problem. The key technical contribution is a method for working with potential functions defined implicitly as the solution of a linear system. The result is robust in the sense that a small change in the probabilities used by the algorithm results in a small change in the upper bound on the competitive ratio. The above result has two important implications. Firstly this yields an $\alpha_k$-competitive memoryless algorithm for the weighted $k$-server problem on uniform spaces. This is the first competitive algorithm for $k>2$ which is memoryless. Secondly, this helps us prove that the Harmonic algorithm, which chooses probabilities in inverse proportion to weights, has a competitive ratio of $k\alpha_k$.Comment: Published at the 54th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2013

Metrical Service Systems with Multiple Servers

We study the problem of metrical service systems with multiple servers (MSSMS), which generalizes two well-known problems -- the $k$-server problem, and metrical service systems. The MSSMS problem is to service requests, each of which is an $l$-point subset of a metric space, using $k$ servers, with the objective of minimizing the total distance traveled by the servers. Feuerstein initiated a study of this problem by proving upper and lower bounds on the deterministic competitive ratio for uniform metric spaces. We improve Feuerstein's analysis of the upper bound and prove that his algorithm achieves a competitive ratio of $k({{k+l}\choose{l}}-1)$. In the randomized online setting, for uniform metric spaces, we give an algorithm which achieves a competitive ratio $\mathcal{O}(k^3\log l)$, beating the deterministic lower bound of ${{k+l}\choose{l}}-1$. We prove that any randomized algorithm for MSSMS on uniform metric spaces must be $\Omega(\log kl)$-competitive. We then prove an improved lower bound of ${{k+2l-1}\choose{k}}-{{k+l-1}\choose{k}}$ on the competitive ratio of any deterministic algorithm for $(k,l)$-MSSMS, on general metric spaces. In the offline setting, we give a pseudo-approximation algorithm for $(k,l)$-MSSMS on general metric spaces, which achieves an approximation ratio of $l$ using $kl$ servers. We also prove a matching hardness result, that a pseudo-approximation with less than $kl$ servers is unlikely, even for uniform metric spaces. For general metric spaces, we highlight the limitations of a few popular techniques, that have been used in algorithm design for the $k$-server problem and metrical service systems.Comment: 18 pages; accepted for publication at COCOON 201

Approximating the Regular Graphic TSP in near linear time

We present a randomized approximation algorithm for computing traveling salesperson tours in undirected regular graphs. Given an $n$-vertex, $k$-regular graph, the algorithm computes a tour of length at most $\left(1+\frac{7}{\ln k-O(1)}\right)n$, with high probability, in $O(nk \log k)$ time. This improves upon a recent result by Vishnoi (\cite{Vishnoi12}, FOCS 2012) for the same problem, in terms of both approximation factor, and running time. The key ingredient of our algorithm is a technique that uses edge-coloring algorithms to sample a cycle cover with $O(n/\log k)$ cycles with high probability, in near linear time. Additionally, we also give a deterministic $\frac{3}{2}+O\left(\frac{1}{\sqrt{k}}\right)$ factor approximation algorithm running in time $O(nk)$.Comment: 12 page

Clinical profile, risk factors and aetiology of young stroke: a tertiary care hospital based study from the Sub-Himalayan region in North India

Background: Rapid urbanisation of rural areas is predicted to increase the incidence of risk factors for vascular events like stroke. There is scarcity of literature addressing issue of stroke from Sub-Himalayan region in North India.Methods:The study was conducted in the department of medicine, R. P. govt. medical college, Kangra, Himachal Pradesh. Consecutive patients between the age of 15-45 years presenting with signs and symptoms of stroke in a duration of one year were included in the study. CT scan-head and lipid profile was done in all patients. Other relevant investigations to rule out aetiology were undertaken.Results: Thirty two patients with the mean age of 41.1 ± 5.41 years were recruited. The incidence of stroke in young forming 8.55% of the total stroke patients (374). There were larger proportion of male patients with a ratio of 3:1.16   patients (50%) presented between 6 am and 12 pm in the   morning hours of day. Maximum patients presented in winter months from November to January. Average delay of presentation to hospital was 30.8 hours. 19 patients (59.3%) presented with infarct. Most common symptom reported was weakness in 18 (56.2%). Predominant traditional risk factors observed was hypertension in 18 (53.1%). Hyperhomocysteinemia was seen in 4 patients (12.5%). Primary antiphospholipid antibody syndrome was seen in 2 (6.25%).Conclusion:This study demonstrated predominant presence of conventional risk factors in young strokes. There was substantial time delay of presentation. Majority of patients presented in winter months. Prevention of vascular risk factors as well as issue of factors leading to delay in presentation needs to be addressed.

Study of the profile of stroke in a tertiary-care hospital in the sub-Himalayan region in north India

Background: Rapid urbanization of rural areas is predicted to increase the incidence of risk factors for vascular events such as stroke among the ruralites. A different culture, beliefs, terrain, and climatic conditions of Himachal Pradesh may have an impact on the profile of stroke. Objectives: To study the profile and the various risk factors of stroke in the sub-Himalayan region of north India. Material and Methods: It was an observational cross-sectional study conducted at the Department of Medicine, R.P. Government Medical College, Kangra, Himachal Pradesh, for a duration of 12 months, from June 2012 to May 2013. Consecutive patients presenting to the hospital with signs and symptoms of stroke were included in the study. Detailed history and clinical examination was carried out in all patients. CT scan, routine blood examination, and lipid profile were evaluated in all patients. Results: Total number of patients who presented with stroke in a year was 374. It formed 4.0% of the total hospital admissions in medical wards. The mean age of stroke patients was 66.17±12.9 years. Of the total patients, 254 (67.9%) were males and 120 (32%) were females; 127 patients (33.9%) presented between 6 am and 12 pm. The majority of patients presented in winter months, from November to January. Average delay in the presentation to hospital was 29 h. Only 79 (21.1%) patients presented within 3 h. Among the patients, 342 (91.4%) belonged to rural area, 61.4% had an infarct, and 38.6% had intracerebral bleed. The most common symptoms reported were weakness in 276 (73%) followed by speech abnormality in 53%. Hypertension as a risk factor was found in 174 (46.5%); 155 patients (41.4%) were smokers; and diabetes was present in 61 patients (16.4%). Average cholesterol level was 176±54.99 mg/dl, and average triglyceride level was 339 mg/dl. Conclusions: The major strength in our study was the predominance of rural population. The state has witnessed an increase in the incidence of stroke. Elderly population is predominantly affected. Average delay in presentation was 29 h, which is substantially high. Majority of the events occurred in winter months

Comparative Genomics, Evolutionary Epidemiology, and RBD-hACE2 Receptor Binding Pattern in B.1.1.7 (Alpha) and B.1.617.2 (Delta) Related to Their Pandemic Response in UK and India

BACKGROUND: The massive increase in COVID-19 infection had generated a second wave in India during May-June 2021 with a critical pandemic situation. The Delta variant (B.1.617.2) was a significant factor during the second wave. Conversely, the UK had passed through the crucial phase of the pandemic from November to December 2020 due to B.1.1.7. The study tried to comprehend the pandemic response in the UK and India to the spread of the B.1.1.7 (Alpha, UK) variant and B.1.617.2 (Delta, India) variant. METHODS: This study was performed in three directions to understand the pandemic response of the two emerging variants. First, we served comparative genomics, such as genome sequence submission patterns, mutational landscapes, and structural landscapes of significant mutations (N501Y, D614G, L452R, E484Q, and P681R). Second, we performed evolutionary epidemiology using molecular phylogenetics, scatter plots of the cluster evaluation, country-wise transmission pattern, and frequency pattern. Third, the receptor binding pattern was analyzed using the Wuhan reference strain and the other two variants. RESULTS: The study analyzed the country-wise and region-wise genome sequences and their submission pattern, molecular phylogenetics, scatter plot of the cluster evaluation, country-wise geographical distribution and transmission pattern, frequency pattern, entropy diversity, and mutational landscape of the two variants. The structural pattern was analyzed in the N501Y, D614G L452R, E484Q, and P681R mutations. The study found increased molecular interactivity between hACE2-RBD binding of B.1.1.7 and B.1.617.2 compared to the Wuhan reference strain. Our receptor binding analysis showed a similar indication pattern for hACE2-RBD of these two variants. However, B.1.617.2 offers slightly better stability in the hACE2-RBD binding pattern through MD simulation than B.1.1.7. CONCLUSION: The increased hACE2-RBD binding pattern of B.1.1.7 and B.1.617.2 might help to increase the infectivity compared to the Wuhan reference strain

Multi-Class ECG Feature Importance Rankings: Cardiologists vs. Algorithms

Cardiologists have been using electrocardiogram features to diagnose a wide variety of heart conditions for many decades. There are also numerous algorithms that rank feature importance for a particular classification task. However, different algorithms often give quite different feature rankings. Therefore, we compared the feature importance rankings obtained by various algorithms with the features that cardiologists use for diagnosis

Structural Integrity Assessment of Weld for Joining Waveguide to Annular Linear Induction Pump Subjected to Vibration

Annular Linear Induction Pump (ALIP) is employed for low flow rate pumping of liquid metals because of its maintenance free operation.  In order to monitor pump vibration during operation, a waveguide with accelerometer combination is employed.  The waveguide is a SS rod of 300 mm length and 20 mm diameter which is provided with a threaded provision at one end for mounting the accelerometer.  The other end of the waveguide is welded to the shell of the ALIP of 3 mm thickness. These waveguides are to be attached to the ALIP in different orientations. The weld connecting the waveguide to the shell of ALIP is subjected to fatigue loading caused due to pump vibration. This paper discusses the analysis carried out to determine the fatigue life of the weld using ASME SECTION VIII DIVISION 2. Keywords. ALIP; vibration; waveguide; weld; fatigue

PTB-XL+, a comprehensive electrocardiographic feature dataset

Machine learning (ML) methods for the analysis of electrocardiography (ECG) data are gaining importance, substantially supported by the release of large public datasets. However, these current datasets miss important derived descriptors such as ECG features that have been devised in the past hundred years and still form the basis of most automatic ECG analysis algorithms and are critical for cardiologists’ decision processes. ECG features are available from sophisticated commercial software but are not accessible to the general public. To alleviate this issue, we add ECG features from two leading commercial algorithms and an open-source implementation supplemented by a set of automatic diagnostic statements from a commercial ECG analysis software in preprocessed format. This allows the comparison of ML models trained on clinically versus automatically generated label sets. We provide an extensive technical validation of features and diagnostic statements for ML applications. We believe this release crucially enhances the usability of the PTB-XL dataset as a reference dataset for ML methods in the context of ECG data

A Ten-year Retrospective Study of Nasal Bone Fractures at a Tertiary Care Hospital of Nepal

 Introduction: Nasal bone fracture occurs due to its vulnerable position and reduced biomechanical resistance to traumas. If not timely treated, it can result in permanent functional and esthetic damage. Methods: A retrospective and cross-sectional study conducted on 91 patients above 17 years of age with nasal bone fractures in the Department of Otorhinolaryngology and Head and Neck surgery of a tertiary care hospital in Kavre. Results: Road traffic accident was the most common cause of fracture (45.1%) followed by fall (36.3%), violence (13.2%), sports-related accidents (4.4%) and occupational accidents (1.1%). Class I fracture was seen in 70 (76.9%), Class II in 17 (18.7%), and Class III in 4 (4.4%). A closed reduction procedure was performed in 74 (81.30%) of the cases, closed reduction with septoplasty was done in 10 (11%), closed reduction with augmentation rhinoplasty was performed for 3 (3.3%), closed reduction with inferior turbinoplasty was required in 3 (3.3%) whereas closed reduction with debridement was done in 1(1.1%). Conclusion: Nasal bone fracture is a complex clinical issue which needs to be addressed early. Violence prevention programs along with drinking and driving campaigns need to be more strengthened to decrease the alarmingly high frequency of nasal bone fracture in the current scenario