Search

This article presents a low-rank decomposition algorithm based on subsampling of matrix entries. The proposed algorithm first computes rank-revealing decompositions of submatrices with a blocked adaptive cross approximation (BACA) algorithm, and then applies a hierarchical merge operation via truncated singular value decompositions (H-BACA). The proposed algorithm significantly improves the convergence of the baseline ACA algorithm and achieves reduced computational complexity compared to the traditional decompositions such as rank-revealing QR. Numerical results demonstrate the efficiency, accuracy, and parallel scalability of the proposed algorithm.

We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the execution time are drastically reduced compared to standard dense linear algebra routines. We consider both the general H matrix hierarchical format as well as Hierarchically Semi-Separable (HSS) matrices. Furthermore, we investigate the impact of several preprocessing and clustering techniques on the hierarchical matrix compression. Effective clustering of the input leads to a ten-fold increase in efficiency of the compression. The algorithms are implemented using the STRUMPACK solver library. These results confirm that - with correct tuning of the hyperparameters - classification using kernel ridge regression with the compressed matrix does not lose prediction accuracy compared to the exact - not compressed - kernel matrix and that our approach can be extended to O(1M) datasets, for which computation with the full kernel matrix becomes prohibitively expensive. We present numerical experiments in a distributed memory environment up to 1,024 processors of the NERSC's Cori supercomputer using well-known datasets to the machine learning community that range from dimension 8 up to 784.

Can the behavior of a random matrix be improved by modifying a small fraction of its entries? Consider a random matrix A with i.i.d. entries. We show that the operator norm of A can be reduced to the optimal order O(n) by zeroing out a small submatrix of A if and only if the entries have zero mean and finite variance. Moreover, we obtain an almost optimal dependence between the size of the removed submatrix and the resulting operator norm. Our approach utilizes the cut norm and Grothendieck–Pietsch factorization for matrices, and it combines the methods developed recently by C. Le and R. Vershynin and by E. Rebrova and K. Tikhomirov.

Inferior alveolar nerve block (IANB) is one of the most common procedures in operative dentistry, and a deep understanding of the normal anatomical variation of the pterygomandibular space (PM) is essential for its safe and successful administration. This cadaveric anatomical study aimed to use A-silicone injections to evaluate the volume of the PM. This study was conducted using 46 human cadaver heads (25 males and 21 females). A craniometric analysis was performed using the cadavers' ages, the number of silicone cartridges (carpules) used to fill the pterygomandibular space, Izard's Facial Index (FI), and the Cranial Index (CI). A Halstead mandibular block was performed by injecting 1.7 mL A-silicone cartridges (as an equivalent to standard local aesthetic carpules volume) into the PM. The cured silicone was extracted from the dissected mandibles. The volume (length, width, and thickness) of the extracted silicone and the number of silicone cartridges used to fill the space were evaluated. The results showed that there are statistically significant positive correlations between the CI and the width of the right PM, as well as the width and length of the left PM. A statistically significant correlation was found between the width of the left PM and the age of the cadaveric heads; the higher the age, the thicker the space on both sides. The volume of the PM corresponded to 1.5 cartridges on average.

In recent years, an increasing amount of attention has been paid to medicinal products as possible risk factors in the development of eye diseases. The frequency of diagnosed drug-induced uveitis is growing yearly, which can be attributed to the appearance of new drugs - biological agents (immune checkpoint inhibitors, BRAF and MEK inhibitors, vascular endothelial growth factor inhibitors, tumor necrosis factor-α inhibitors), as well as systemic bisphosphonates and some antiviral drugs. The time interval between the beginning of the drug use and the appearance of uveitis symptoms varies from several days to months. Common symptoms include eye pain, photophobia, the appearance of floating opacities, and reduced vision associated with active inflammatory changes in the retina and optic nerve and outcomes of those inflammations. Timely diagnosis, cancellation of the drug that caused uveitis and appointment of adequate anti-inflammatory therapy in most cases effectively stops the symptoms of the disease, which determines the relevance of attention to the prevalence, pathogenesis, diagnosis and treatment of drug-induced uveitis.

Glaucoma is seen as a heterogeneous group of diseases characterized by optical neuropathy with associated visual field loss; one of the main risk factors for its development is increased intraocular pressure (IOP). In the case of drug-induced glaucoma (DIG), patients develop elevated IOP, optic neuropathy and visual field defects associated with the use of certain drugs. Corticosteroids are one of the most well-known classes of drugs that can cause an increase in IOP through the open-angle mechanism. Drug-induced glaucoma, which develops similarly to open-angle glaucoma, can also be caused by some non-steroidal anti-inflammatory agents, antibodies to the endothelial growth factor, etc. Classes of drugs that can cause angle-closure glaucoma include topical anticholinergic or sympathomimetic drops, tricyclic antidepressants, monoamine oxidase inhibitors, antihistamines, antiparkinsonian drugs, antipsychotic drugs, antispasmodics. Products containing sulfa group drugs can cause DIG due to a different closing angle mechanism involving a forward rotation of the ciliary body. It is important for medical practitioners to be aware of this unwanted drug reaction in order to prevent, detect and treat DIG. In the case of drug-induced increase in IOP, if the underlying disease allows discontinuation of drugs, this measure usually leads to normalization of IOP. In cases when the patient's IOP does not normalize after discontinuation of steroids or when they must continue to take corticosteroids, the administration of topical drugs for the treatment of glaucoma should be considered.

Drug-induced dysphonia is a non-life-threatening adverse drug reaction, however, this complication can significantly worsen the quality of life of patients, especially those in voice-speaking professions. The aim of the work was to search for information about the prevalence, etiology, pathogenesis, and features of treatment and prevention of drug-induced dysphonia. In the case of some drugs, the true prevalence may be higher than described in the literature, due to the fact that dysphonia is in most cases mild, reversible and, in comparison with other undesirable drug reactions, rarely attracts the attention of both the patient and practitioners.

One type of non-allergic non-infectious rhinitis is represented by a heterogeneous group of rhinitis medicamentosa, which can be divided into several pathogenetic types. The most common rebound nasal congestion associated with the use of topical decongestants. Excessive use of intranasal decongestants leads to a decrease in the number of alpha-adrenoreceptors on the surface of cell membranes and uncoupling their connection with the G-protein and the development of tachyphylaxis. To prevent the development of rebound nasal congestion caused by topical decongestants, it is important to limit the frequency of their use. In most cases, the duration of the use of vasoconstrictor drugs should be limited to 5-7 days, according to Patient information leaflets for the drugs. However, in patients who have had a history of episodes of rebound nasal congestion, which develops including the previously indicated periods, the duration of decongestant therapy should be limited to 3 days. Rhinitis associated with local inflammation is caused by the intake of acetylsalicylic acid (ASA) or other non-steroidal anti-inflammatory drugs. Currently, the so-called "aspirin triad" is well known - a combination of bronchial asthma, rhinosinusitis (often polyposis) and intolerance to ASA. Neurogenic rhinitis develops due to the use of drugs that violate vascular tone, for example, antihypertensive drugs or type 5 phosphodiesterase inhibitors. Drug-induced rhinitis has a significant impact on the patient's quality of life: nasal congestion, rhinorrhea, secondary night apnea, insomnia as a result of nasal breathing disturbances, headaches, irritability, weakness after sleepless nights disturb patients to a large extent. Timely diagnosis and withdrawal of a provocative drug, the use of topical corticosteroids in case of severe rhinitis are the basis of the treatment of rhinitis medicamentosa. In severe cases, there is a need, including surgical treatment, such as, for example, submucosal laser destruction of the lower nasal concha.

Drug-induced optic neuropathy is a group of disorders in which medications cause degeneration of the optic nerve. The true prevalence of drug-induced neuropathy has not been studied, although the percentage of patients who develop optic nerve damage is known for individual medications. The common pathophysiological mechanisms are believed to be mitochondrial damage and imbalance of intracellular and extracellular free radical homeostasis. Typical symptoms of drug-induced neuropathy are reduced visual acuity in the central area, which is often bilateral, visual field disturbances, dyschromatopsia, and edema of the optic nerve head. Early detection of drug-induced optic neuropathy can potentially prevent or minimize serious complications. For patients who develop drug-induced optic neuropathy, treatment is based on timely diagnosis and cancellation of the provoking drug. In most patients, vision usually recovers a few weeks or months after discontinuation of previous therapy, but there have been cases of irreversible vision loss. In addition to withdrawal of the drug that caused optic nerve lesion, treatment of drug-induced neuropathy may include use of drugs and treatment methods prescribed by neurologists for peripheral neuropathy, however, such treatment is seldom based on evidence.