Stable Recovery Of Sparse Vectors From Random Sinusoidal Feature Maps

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a random Gaussian matrix, and then computing an element-wise sinusoid. Theoretical analysis shows that collecting a sufficient number of such features can be reliably used for subsequent inference in kernel classification and regression. In this work, we demonstrate that with a mild increase in the dimension of the embedding, it is also possible to reconstruct the data vector from such random sinusoidal features, provided that the underlying data is sparse enough. In particular, we propose a numerically stable algorithm for reconstructing the data vector given the nonlinear features, and analyze its sample complexity. Our algorithm can be extended to other types of structured inverse problems, such as demixing a pair of sparse (but incoherent) vectors. We support the efficacy of our approach via numerical experiments

Reconstruction from Periodic Nonlinearities, With Applications to HDR Imaging

We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to compressive sensing-based signal and image acquisition systems. Our techniques can be potentially useful for reducing the measurement complexity of high dynamic range (HDR) imaging systems, with little loss in reconstruction quality. Several numerical experiments on real data demonstrate the effectiveness of our approach

La comparación del dolor de cabeza en la medicina iraní moderna y tradicional

Headache is one of the most common pains in during life all of the human, which even children sometimes suffer from it. In modern medicine, headaches are broadly classified into two primary and secondary. Primary headaches usually are headaches in which the illness or other factor has not caused headache, and include cluster headaches - migraines and tension-type headaches and chronic daily headaches. Secondary headaches have many causes and pathologies (disease or pathology) that affected by disease or problems in other parts of the body, or intracranial disease, such as meningitis, which has been shown as a headache. Fortunately, about 98% of the headaches are benign and improvable and 1to 2 percent of the headaches occur due to brain tumors or brain damage. According to the World Health Organization, 64% to 77% of the world’s population experienced headaches at least once in their life, and  50% of the people once a year had headaches. In traditional Iranian medicine, as many as sixty types of headaches in various temperaments: Bilious, Sanguine, phlegmatic and melancholic, by Iranian great scientists such as Avicenna and Hakim Momen, have been investigated and various strategies for prevention and treatment many of them have been recommended. In this research, several studies to search in the authoritative traditional medicine resources and PubMed databases investigated and various mechanisms for the treatment of headache in Iranian traditional medicine have been interpreted.El dolor de cabeza es uno de los dolores más comunes en la vida de todo el ser humano, que incluso los niños a veces sufren. En la medicina moderna, los dolores de cabeza se clasifican ampliamente en dos primarios y secundarios. Los dolores de cabeza primarios generalmente son dolores de cabeza en los que la enfermedad u otro factor no ha causado dolor de cabeza e incluyen dolores de cabeza en racimo: migrañas y dolores de cabeza de tipo tensional y dolores de cabeza crónicos diarios. Los dolores de cabeza secundarios tienen muchas causas y patologías (enfermedades o patologías) que se ven afectadas por enfermedades o problemas en otras partes del cuerpo o enfermedades intracraneales, como la meningitis, que se ha demostrado como un dolor de cabeza. Afortunadamente, alrededor del 98% de los dolores de cabeza son benignos y mejorables y del 1 al 2 por ciento de los dolores de cabeza ocurren debido a tumores cerebrales o daño cerebral. Según la Organización Mundial de la Salud, del 64% al 77% de la población mundial experimentó dolores de cabeza al menos una vez en su vida, y el 50% de las personas una vez al año tenían dolores de cabeza. En la medicina tradicional iraní, se han investigado hasta sesenta tipos de dolores de cabeza en varios temperamentos: biliosos, sangrientos, flemáticos y melancólicos, por grandes científicos iraníes como Avicena y Hakim Momen, y se han investigado varias estrategias para la prevención y el tratamiento, muchos de ellos. recomendado. En esta investigación, se investigaron varios estudios para buscar en los recursos autorizados de la medicina tradicional y las bases de datos PubMed y se han interpretado varios mecanismos para el tratamiento del dolor de cabeza en la medicina tradicional iraní