Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization

We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficients are estimated in alternate steps, keeping the other fixed. Typically, the coefficients are estimated via $\ell_1$ minimization, keeping the dictionary fixed, and the dictionary is estimated through least squares, keeping the coefficients fixed. In this paper, we establish local linear convergence for this variant of alternating minimization and establish that the basin of attraction for the global optimum (corresponding to the true dictionary and the coefficients) is \order{1/s^2}, where $s$ is the sparsity level in each sample and the dictionary satisfies RIP. Combined with the recent results of approximate dictionary estimation, this yields provable guarantees for exact recovery of both the dictionary elements and the coefficients, when the dictionary elements are incoherent.Comment: Local linear convergence now holds under RIP and also more general restricted eigenvalue condition

A CRITICAL REVIEW OF POTAKI (BASELLA ALBA) IN AYURVEDIC TEXTS WITH RECENT STUDIES

Potaki (Basella alba) commonly known as Malabar spinach, is a soft stemmed perinneal vine. It is an edible vine in the family Basellaceae. It is found in tropical Asia and Africa where it is widely used as a leaf vegetable. It is known under various common names like Vine spinach, Climbing spinach, Creeping spinach, Buffalo spinach and Ceylon spinach among others. It grows well under full sunlight in hot, humid climates and in areas lower than 500 metres above sea level. Typical of leaf vegetable, Malabar spinach is high in vitamin A, C and Iron. It is low in calories by volume, but high in protein per calorie. The succulent mucilage is particularly rich source of soluble fiber. In the Indian system of medicine, the plant has immense potential in androgenic activity, antioxidant, nephroprotective, anti-inflammatory and antibacterial activity. The plant has been known to be a demulcent, a diuretic and an emollient action. The entire plant is used in Chinese medicine where it is claimed to reduce fever and neutralise poison. To cure human disease, medicinal plants have been a major source of therapeutic agents since ancient times. The revival of interest in natural drugs started in last decade mainly because of the wide spread belief that natural medicine is healthier than synthetic products. As per WHO, 80% of the population in the world relays on the traditional medicine for treatment of various disease. Therefore evaluation of rich heritage of traditional medicine is essential. In this regard one such plant is Basella alba.

Sternoclavicular joint arthropathy mimicking radiculopathy in a patient with concurrent C4-5 disc herniation

Background Patients with sternoclavicular joint arthropathy, which can result from septic arthritis, often present with localized sternoclavicular pain as well as shoulder pain. Such pain may be similar to the presenting symptoms of cervical intervertebral disc herniation. Clinical presentation A 47-year-old female presented with 1 month of significant pain in the neck as well as right anterior chest and deltoid. The patient was found to have reduced strength in the right deltoid muscle on physical examination. MRI revealed a C4-C5 herniated nucleus pulposus. The patient underwent successful C4-C5 anterior cervical discectomy, but subsequently developed painful swelling in the region of the right sternoclavicular joint with limited motor strength in the right shoulder and arm. A needle biopsy of the mass yielded negative results, but her erythrocyte sedimentation rate (ESR) and C-reactive protein (CRP) numbers did respond to antibiotics, consistent with infection of the sternoclavicular joint. A follow-up CT scan (6.5 months postoperatively) revealed apparent resolution right sternoclavicular joint arthropathy, thought the patient continued to experience pain. 15 months postoperatively, the patient was prescribed methotrexate due to persistent pain and mild weakness arising from a possible rheumatologic inflammation. 19 months postoperatively, the patient had full strength of the right shoulder and arm and visible decrease in swelling at the sternoclavicular joint. More than three years postoperatively, the patient was diagnosed with multiple myeloma, which was appropriately treated. At follow-up four years postoperatively, the patient had an MRI showing new C6-C7 herniated nucleus pulposus, but no longer had any right shoulder or chest pain or associated weakness. Conclusion This case demonstrates that sternoclavicular joint arthropathy results in symptoms that can mimic the presenting symptoms of shoulder or cervical spine pathology, such as shoulder and neck pain, necessitating careful diagnosis and management

Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization

We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficients are estimated in alternate steps, keeping the other fixed. Typically, the coefficients are estimated via ℓ_1 minimization, keeping the dictionary fixed, and the dictionary is estimated through least squares, keeping the coefficients fixed. In this paper, we establish local linear convergence for this variant of alternating minimization and establish that the basin of attraction for the global optimum (corresponding to the true dictionary and the coefficients) is O(1/s^2), where s is the sparsity level in each sample and the dictionary satisfies restricted isometry property. Combined with the recent results of approximate dictionary estimation, this yields provable guarantees for exact recovery of both the dictionary elements and the coefficients, when the dictionary elements are incoherent

An Intelligent Framework for Estimating Software Development Projects using Machine Learning

The IT industry has faced many challenges related to software effort and cost estimation. A cost assessment is conducted after software effort estimation, which benefits customers as well as developers. The purpose of this paper is to discuss various methods for the estimation of software effort and cost in the context of software engineering, such as algorithmic methods, expert judgment methods, analogy-based estimation methods, and machine learning methods, as well as their different aspects. In spite of this, estimation of the effort involved in software development are subject to uncertainty. Several methods have been developed in the literature for improving estimation accuracy, many of which involve the use of machine learning techniques. A machine learning framework is proposed in this paper to address this challenging problem. In addition to being completely independent of algorithmic models and estimation problems, this framework also features a modular architecture. It has high interpretability, learning capability, and robustness to imprecise and uncertain inputs

RFID Based Automatic Shopping Cart

Large grocery stores are nowadays used by millions of people for the acquisition of an enlarging number of products. Product acquisition represents a complex process that comprises time spent in corridors, product location and checkout queues. On the other hand, it is becoming increasingly difficult for retailers to keep their clients loyal and to predict their needs due to the influence of competition and the lack of tools that discriminate consumption patterns. In this article it is presented the proposal of an architecture and solution of an innovative system for the acquisition of products in grocery stores (Intelligent Cart). The Intelligent Cart explores emerging mobile technologies and automatic identification technologies (such as RFID) as a way to improve the quality of services provided by retailers and to augment the consumer value thus allowing to save time and money. Keywords: Automatic Product Identification; Electronic Services; Grocery Stores, RFID, Intelligent car

Universal quantum computation using single qubit discrete-time quantum walk

Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single qubit discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of the scheme is demonstrated by using a set of walk operations on a closed lattice form to implement the universal set of quantum gates on multi-qubit system. We also present a set of experimentally realizable walk operations that can implement Grover's algorithm, quantum Fourier transformation and quantum phase estimation algorithms. Analysis of space and time complexity of the scheme highlights the advantages of quantum walk based model for quantum computation on systems where implementation of quantum walk evolution operations is inherent feature of the system.Comment: 16 papges, 16 figure

Cytological spectrum of granulomatous mastitis: diagnostic and treatment challenges

Background: Granulomatous mastitis (GM) is an inflammatory disease of the breast which clinico- radiologically mimics both inflammatory and malignant lesions. This leads to diagnostic dilemmas and delay in treatment. The aim of the present study was to review the cases diagnosed as granulomatous mastitis on Fine Needle Aspiration Cytology (FNAC) with an objective to co-relate their clinico-radiological findings, histology review where available and follow up treatment received to establish etiology and study the treatment outcome.Methods: Cytologically diagnosed cases of granulomatous mastitis were retrieved and reviewed from August 2015 - July 2017 records. Clinico-radiological co-relation, histology review where available and follow up treatment records were sought for.Results: Around 31.7% (530/1670) cases were reported as malignant, 60.3% (1009/1670) as benign proliferative and 7.9% (131/1670) as inflammatory lesions by breast FNA. 3.1% (51/1670) cases were reported as GM of all breast FNAC and 38% (51/131) of all inflammatory lesions. Follow up was available for 47 cases. Of which 26 (55.3%) cases were diagnosed as Tubercular Granulomatous mastitis (TGM) and 21(44.7%) were idiopathic granulomatous mastitis (IGM).Conclusions: Countries where tuberculosis is endemic, high degree of clinical suspicion and detailed work-up to rule out TGM is essential for all cases of granulomatous mastitis. Authors recommend a multidisciplinary workup with microbiological culture and molecular based tests on FNA material. This retrospective study illustrates that the cause of GM needs to be determined accurately for timely treatment, to avoid unnecessary delays and treatment dilemma in these patients