Iterative actions of normal operators

Let $A$ be a normal operator in a Hilbert space $\mathcal{H}$, and let $\mathcal{G} \subset \mathcal{H}$ be a countable set of vectors. We investigate the relations between $A$, $\mathcal{G}$ , and $L$ that makes the system of iterations $\{A^ng: g\in \mathcal{G},\;0\leq n< L(g)\}$ complete, Bessel, a basis, or a frame for $\mathcal{H}$. The problem is motivated by the dynamical sampling problem and is connected to several topics in functional analysis, including, frame theory and spectral theory. It also has relations to topics in applied harmonic analysis including, wavelet theory and time-frequency analysis.Comment: 14 pages, 0 figure

A Compact Representation of Histopathology Images using Digital Stain Separation & Frequency-Based Encoded Local Projections

In recent years, histopathology images have been increasingly used as a diagnostic tool in the medical field. The process of accurately diagnosing a biopsy sample requires significant expertise in the field, and as such can be time-consuming and is prone to uncertainty and error. With the advent of digital pathology, using image recognition systems to highlight problem areas or locate similar images can aid pathologists in making quick and accurate diagnoses. In this paper, we specifically consider the encoded local projections (ELP) algorithm, which has previously shown some success as a tool for classification and recognition of histopathology images. We build on the success of the ELP algorithm as a means for image classification and recognition by proposing a modified algorithm which captures the local frequency information of the image. The proposed algorithm estimates local frequencies by quantifying the changes in multiple projections in local windows of greyscale images. By doing so we remove the need to store the full projections, thus significantly reducing the histogram size, and decreasing computation time for image retrieval and classification tasks. Furthermore, we investigate the effectiveness of applying our method to histopathology images which have been digitally separated into their hematoxylin and eosin stain components. The proposed algorithm is tested on the publicly available invasive ductal carcinoma (IDC) data set. The histograms are used to train an SVM to classify the data. The experiments showed that the proposed method outperforms the original ELP algorithm in image retrieval tasks. On classification tasks, the results are found to be comparable to state-of-the-art deep learning methods and better than many handcrafted features from the literature.Comment: Accepted for publication in the International Conference on Image Analysis and Recognition (ICIAR 2019

Prescribing patterns in dementia: a multicentre observational study in a German network of CAM physicians

<p>Abstract</p> <p>Background</p> <p>Dementia is a major and increasing health problem worldwide. This study aims to investigate dementia treatment strategies among physicians specialised in complementary and alternative medicine (CAM) by analysing prescribing patterns and comparing them to current treatment guidelines in Germany.</p> <p>Methods</p> <p>Twenty-two primary care physicians in Germany participated in this prospective, multicentre observational study. Prescriptions and diagnoses were reported for each consecutive patient. Data were included if patients had at least one diagnosis of dementia according to the 10th revision of the International Classification of Diseases during the study period. Multiple logistic regression was used to determine factors associated with a prescription of any anti-dementia drug including <it>Ginkgo biloba</it>.</p> <p>Results</p> <p>During the 5-year study period (2004-2008), 577 patients with dementia were included (median age: 81 years (IQR: 74-87); 69% female). Dementia was classified as unspecified dementia (57.2%), vascular dementia (25.1%), dementia in Alzheimer's disease (10.4%), and dementia in Parkinson's disease (7.3%). The prevalence of anti-dementia drugs was 25.6%. The phytopharmaceutical <it>Ginkgo biloba </it>was the most frequently prescribed anti-dementia drug overall (67.6% of all) followed by cholinesterase inhibitors (17.6%). The adjusted odds ratio (AOR) for receiving any anti-dementia drug was greater than 1 for neurologists (AOR = 2.34; CI: 1.59-3.47), the diagnosis of Alzheimer's disease (AOR = 3.28; CI: 1.96-5.50), neuroleptic therapy (AOR = 1.87; CI: 1.22-2.88), co-morbidities hypertension (AOR = 2.03; CI: 1.41-2.90), and heart failure (AOR = 4.85; CI: 3.42-6.88). The chance for a prescription of any anti-dementia drug decreased with the diagnosis of vascular dementia (AOR = 0.64; CI: 0.43-0.95) and diabetes mellitus (AOR = 0.55; CI: 0.36-0.86). The prescription of <it>Ginkgo biloba </it>was associated with sex (female: AOR = 0.41; CI: 0.19-0.89), patient age (AOR = 1.06; CI: 1.02-1.10), treatment by a neurologist (AOR = 0.09; CI: 0.03-0.23), and the diagnosis of Alzheimer's disease (AOR = 0.07; CI: 0.04-0.16).</p> <p>Conclusions</p> <p>This study provides a comprehensive analysis of everyday practice for treatment of dementia in primary care in physicians with a focus on CAM. The prescribing frequency for anti-dementia drugs is equivalent to those found in other German studies, while the administration of <it>Ginkgo biloba </it>is significantly higher.</p

A Model of Late Long-Term Potentiation Simulates Aspects of Memory Maintenance

Late long-term potentiation (L-LTP) appears essential for the formation of long-term memory, with memories at least partly encoded by patterns of strengthened synapses. How memories are preserved for months or years, despite molecular turnover, is not well understood. Ongoing recurrent neuronal activity, during memory recall or during sleep, has been hypothesized to preferentially potentiate strong synapses, preserving memories. This hypothesis has not been evaluated in the context of a mathematical model representing biochemical pathways important for L-LTP. I incorporated ongoing activity into two such models: a reduced model that represents some of the essential biochemical processes, and a more detailed published model. The reduced model represents synaptic tagging and gene induction intuitively, and the detailed model adds activation of essential kinases by Ca. Ongoing activity was modeled as continual brief elevations of [Ca]. In each model, two stable states of synaptic weight resulted. Positive feedback between synaptic weight and the amplitude of ongoing Ca transients underlies this bistability. A tetanic or theta-burst stimulus switches a model synapse from a low weight to a high weight stabilized by ongoing activity. Bistability was robust to parameter variations. Simulations illustrated that prolonged decreased activity reset synapses to low weights, suggesting a plausible forgetting mechanism. However, episodic activity with shorter inactive intervals maintained strong synapses. Both models support experimental predictions. Tests of these predictions are expected to further understanding of how neuronal activity is coupled to maintenance of synaptic strength.Comment: Accepted to PLoS One. 8 figures at en

Antiinflammatory Therapy with Canakinumab for Atherosclerotic Disease

Background: Experimental and clinical data suggest that reducing inflammation without affecting lipid levels may reduce the risk of cardiovascular disease. Yet, the inflammatory hypothesis of atherothrombosis has remained unproved. Methods: We conducted a randomized, double-blind trial of canakinumab, a therapeutic monoclonal antibody targeting interleukin-1β, involving 10,061 patients with previous myocardial infarction and a high-sensitivity C-reactive protein level of 2 mg or more per liter. The trial compared three doses of canakinumab (50 mg, 150 mg, and 300 mg, administered subcutaneously every 3 months) with placebo. The primary efficacy end point was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death. RESULTS: At 48 months, the median reduction from baseline in the high-sensitivity C-reactive protein level was 26 percentage points greater in the group that received the 50-mg dose of canakinumab, 37 percentage points greater in the 150-mg group, and 41 percentage points greater in the 300-mg group than in the placebo group. Canakinumab did not reduce lipid levels from baseline. At a median follow-up of 3.7 years, the incidence rate for the primary end point was 4.50 events per 100 person-years in the placebo group, 4.11 events per 100 person-years in the 50-mg group, 3.86 events per 100 person-years in the 150-mg group, and 3.90 events per 100 person-years in the 300-mg group. The hazard ratios as compared with placebo were as follows: in the 50-mg group, 0.93 (95% confidence interval [CI], 0.80 to 1.07; P = 0.30); in the 150-mg group, 0.85 (95% CI, 0.74 to 0.98; P = 0.021); and in the 300-mg group, 0.86 (95% CI, 0.75 to 0.99; P = 0.031). The 150-mg dose, but not the other doses, met the prespecified multiplicity-adjusted threshold for statistical significance for the primary end point and the secondary end point that additionally included hospitalization for unstable angina that led to urgent revascularization (hazard ratio vs. placebo, 0.83; 95% CI, 0.73 to 0.95; P = 0.005). Canakinumab was associated with a higher incidence of fatal infection than was placebo. There was no significant difference in all-cause mortality (hazard ratio for all canakinumab doses vs. placebo, 0.94; 95% CI, 0.83 to 1.06; P = 0.31). Conclusions: Antiinflammatory therapy targeting the interleukin-1β innate immunity pathway with canakinumab at a dose of 150 mg every 3 months led to a significantly lower rate of recurrent cardiovascular events than placebo, independent of lipid-level lowering. (Funded by Novartis; CANTOS ClinicalTrials.gov number, NCT01327846.

Improving dimension estimates for Furstenberg-type sets

In this paper we study the problem of estimating the generalized Hausdorff dimension of Furstenberg sets in the plane. For α ∈ (0, 1&#93;, a set F in the plane is said to be an α-Furstenberg set if for each direction e there is a line segment ℓe in the direction of e for which dimH (ℓe ∩ F) ≥ α. It is well known that dimH (F) ≥ max {2 α, α + frac(1, 2)}, and it is also known that these sets can have zero measure at their critical dimension. By looking at general Hausdorff measures Hh defined for doubling functions, that need not be power laws, we obtain finer estimates for the size of the more general h-Furstenberg sets. Further, this approach allow us to sharpen the known bounds on the dimension of classical Furstenberg sets. The main difficulty we had to overcome, was that if Hh (F) = 0, there always exists g ≺ h such that Hg (F) = 0 (here ≺ refers to the natural ordering on general Hausdorff dimension functions). Hence, in order to estimate the measure of general Furstenberg sets, we have to consider dimension functions that are a true step down from the critical one. We provide rather precise estimates on the size of this step and by doing so, we can include a family of zero dimensional Furstenberg sets associated to dimension functions that grow faster than any power function at zero. With some additional growth conditions on these zero dimensional functions, we extend the known inequalities to include the endpoint α = 0. © 2009 Elsevier Inc. All rights reserved.Fil:Molter, U. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Rela, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina