Continuity of Local Time: An applied perspective

Continuity of local time for Brownian motion ranks among the most notable mathematical results in the theory of stochastic processes. This article addresses its implications from the point of view of applications. In particular an extension of previous results on an explicit role of continuity of (natural) local time is obtained for applications to recent classes of problems in physics, biology and finance involving discontinuities in a dispersion coefficient. The main theorem and its corollary provide physical principles that relate macro scale continuity of deterministic quantities to micro scale continuity of the (stochastic) local time.Comment: To appear in: "The fascination of Probability, Statistics and Their Applications. In honour of Ole E. Barndorff-Nielsen on his 80th birthday

Gender differences in delay time for acute myocardial infarction in a Hispanic population

Introduction: There are limited published data on minority populations, especially Hispanics, describing the onset of acute myocardial infarction (AMI) symptoms and time to treatment. The aim of this study is to determine if a difference exists between gender and delay time in Puerto Rican patients hospitalized with an initial acute myocardial infarction

Risk factors for delay in symptomatic presentation: a survey of cancer patients

Background: Delay in symptomatic presentation leading to advanced stage at diagnosis may contribute to poor cancer survival. To inform public health approaches to promoting early symptomatic presentation, we aimed to identify risk factors for delay in presentation across several cancers. Methods: We surveyed 2371 patients with 15 cancers about nature and duration of symptoms using a postal questionnaire. We calculated relative risks for delay in presentation (time from symptom onset to first presentation >3 months) by cancer, symptoms leading to diagnosis and reasons for putting off going to the doctor, controlling for age, sex and deprivation group. Results: Among 1999 cancer patients reporting symptoms, 21% delayed presentation for >3 months. Delay was associated with greater socioeconomic deprivation but not age or sex. Patients with prostate (44%) and rectal cancer (37%) were most likely to delay and patients with breast cancer least likely to delay (8%). Urinary difficulties, change of bowel habit, systemic symptoms (fatigue, weight loss and loss of appetite) and skin symptoms were all common and associated with delay. Overall, patients with bleeding symptoms were no more likely to delay presentation than patients who did not have bleeding symptoms. However, within the group of patients with bleeding symptoms, there were significant differences in risk of delay by source of bleeding: 35% of patients with rectal bleeding delayed presentation, but only 9% of patients with urinary bleeding. A lump was a common symptom but not associated with delay in presentation. Twenty-eight percent had not recognised their symptoms as serious and this was associated with a doubling in risk of delay. Embarrassment, worry about what the doctor might find, being too busy to go to the doctor and worry about wasting the doctor’s time were also strong risk factors for delay, but were much less commonly reported (<6%). Interpretation: Approaches to promote early presentation should aim to increase awareness of the significance of cancer symptoms and should be designed to work for people of the lowest socioeconomic status. In particular, awareness that rectal bleeding is a possible symptom of cancer should be raised

Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets

Frustration refers to competition between different interactions that cannot be simultaneously satisfied, a familiar feature in many magnetic solids. Strong frustration results in highly degenerate ground states, and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism are characterizing the fluctuating spin-liquid regime and determining the mechanism of eventual order at lower temperature. Here, we study a model of a diamond lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration a massive ground state degeneracy develops amongst spirals whose propagation wavevectors reside on a continuous two-dimensional ``spiral surface'' in momentum space. We argue that an important ordering mechanism is entropic splitting of the degenerate ground states, an elusive phenomena called order-by-disorder. A broad ``spiral spin-liquid'' regime emerges at higher temperatures, where the underlying spiral surface can be directly revealed via spin correlations. We discuss the agreement between these predictions and the well characterized spinel MnSc2S4

Perivascular Spaces Segmentation in Brain MRI Using Optimal 3D Filtering

Perivascular Spaces (PVS) are a recently recognised feature of Small Vessel Disease (SVD), also indicating neuroinflammation, and are an important part of the brain's circulation and glymphatic drainage system. Quantitative analysis of PVS on Magnetic Resonance Images (MRI) is important for understanding their relationship with neurological diseases. In this work, we propose a segmentation technique based on the 3D Frangi filtering for extraction of PVS from MRI. Based on prior knowledge from neuroradiological ratings of PVS, we used ordered logit models to optimise Frangi filter parameters in response to the variability in the scanner's parameters and study protocols. We optimized and validated our proposed models on two independent cohorts, a dementia sample (N=20) and patients who previously had mild to moderate stroke (N=48). Results demonstrate the robustness and generalisability of our segmentation method. Segmentation-based PVS burden estimates correlated with neuroradiological assessments (Spearman's $\rho$ = 0.74, p $<$ 0.001), suggesting the great potential of our proposed metho

On finite monoids of cellular automata.

For any group G and set A, a cellular automaton over G and A is a transformation τ:AG→AGτ:AG→AG defined via a finite neighbourhood S⊆GS⊆G (called a memory set of ττ) and a local function μ:AS→Aμ:AS→A. In this paper, we assume that G and A are both finite and study various algebraic properties of the finite monoid CA(G,A)CA(G,A) consisting of all cellular automata over G and A. Let ICA(G;A)ICA(G;A) be the group of invertible cellular automata over G and A. In the first part, using information on the conjugacy classes of subgroups of G, we give a detailed description of the structure of ICA(G;A)ICA(G;A) in terms of direct and wreath products. In the second part, we study generating sets of CA(G;A)CA(G;A). In particular, we prove that CA(G,A)CA(G,A) cannot be generated by cellular automata with small memory set, and, when G is finite abelian, we determine the minimal size of a set V⊆CA(G;A)V⊆CA(G;A) such that CA(G;A)=⟨ICA(G;A)∪V⟩CA(G;A)=⟨ICA(G;A)∪V⟩

Evolutionary-game-based dynamical tuning for multi-objective model predictive control

Model predictive control (MPC) is one of the most used optimization-based control strategies for large-scale systems, since this strategy allows to consider a large number of states and multi-objective cost functions in a straightforward way. One of the main issues in the design of multi-objective MPC controllers, which is the tuning of the weights associated to each objective in the cost function, is treated in this work. All the possible combinations of weights within the cost function affect the optimal result in a given Pareto front. Furthermore, when the system has time-varying parameters, e.g., periodic disturbances, the appropriate weight tuning might also vary over time. Moreover, taking into account the computational burden and the selected sampling time in the MPC controller design, the computation time to find a suitable tuning is limited. In this regard, the development of strategies to perform a dynamical tuning in function of the system conditions potentially improves the closed-loop performance. In order to adapt in a dynamical way the weights in the MPC multi-objective cost function, an evolutionary-game approach is proposed. This approach allows to vary the prioritization weights in the proper direction taking as a reference a desired region within the Pareto front. The proper direction for the prioritization is computed by only using the current system values, i.e., the current optimal control action and the measurement of the current states, which establish the system cost function over a certain point in the Pareto front. Finally, some simulations of a multi-objective MPC for a real multi-variable case study show a comparison between the system performance obtained with static and dynamical tuning.Peer ReviewedPostprint (author's final draft

Proteomic analysis of early diabetic retinopathy reveals mediators of neurodegenerative brain diseases

© 2018 The Authors. PURPOSE. Current evidence suggests that retinal neurodegeneration is an early event in the pathogenesis of diabetic retinopathy. Our main goal was to examine whether, in the diabetic human retina, common proteins and pathways are shared with brain neurodegenerative diseases. METHODS. A proteomic analysis was performed on three groups of postmortem retinas matched by age: nondiabetic control retinas (n = 5), diabetic retinas without glial activation (n = 5), and diabetic retinas with glial activation (n = 5). Retinal lysates from each group were pooled and run on an SDS-PAGE gel. Bands were analyzed sequentially by liquid chromatography-mass spectrometry (LC/MS) using an Orbitrap Mass Spectrometer. RESULTS. A total of 2190 proteins were identified across all groups. To evaluate the association of the identified proteins with neurological signaling, significant signaling pathways belonging to the category ‘‘Neurotransmitters and Other Nervous System Signaling” were selected for analysis. Pathway analysis revealed that ‘‘Neuroprotective Role of THOP1 in Alzheimer’s Disease” and ‘‘Unfolded Protein Response” pathways were uniquely enriched in control retinas. By contrast, ‘‘Dopamine Degradation” and ‘‘Parkinson’s Signaling” were enriched only in diabetic retinas with glial activation. The ‘‘Neuregulin Signaling,” “Synaptic Long Term Potentiation,” and “Amyloid Processing” pathways were enriched in diabetic retinas with no glial activation. CONCLUSIONS. Diabetes-induced retinal neurodegeneration and brain neurodegenerative diseases, such as Alzheimer’s and Parkinson’s diseases, share common pathogenic pathways. These findings suggest that the study of neurodegeneration in the diabetic retina could be useful to further understand the neurodegenerative processes that occur in the brain of persons with diabetes