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Prediction of depression relapse using machine learning with administrative data: Balancing complexity and simplicity
No full textDepression is a mental disorder with a high lifetime prevalence and one of the leading causes of disability worldwide. As many patients experience another depressive episode after being treated, predictive monitoring for the risk of relapse is essential for healthcare professionals to be able to follow up on patients and intervene early. However, automatically monitoring these large groups requires additional considerations going beyond predictive performance, such as data availability and interpretability. In the present paper, we study the suitability of using readily available administrative data for this prediction task. We contrast a logistic regression model containing only a small number of predictors on demographics, medication, and estimated depression severity with regularized regression and XGBoost models incorporating a large number of predictors describing individual treatment and social information. Our results demonstrate that the inclusion of more detailed input does not result in a significant improvement in performance when compared to simpler regression models. In similar data types, we therefore recommend to primarily focus on a small interpretable model
Semidefinite approximations for bicliques and bi-independent pairs
Get PDFWe investigate some graph parameters dealing with bi-independent pairs (A, B) in a bipartite graph G= (V1 ∪ V2,E), that is, pairs (A, B) where A⊆ V1, B⊆ V2, and A∪ B are independent. These parameters also allow us to study bicliques in general graphs. When maximizing the cardinality |A∪ B|, one finds the stability number α(G), well-known to be polynomial-time computable. When maximizing the product |A| · |B|, one finds the parameter g(G), shown to be NP-hard by Peeters in 2003, and when maximizing the ratio |A| · |B|=|A∪ B|, one finds h(G), introduced by Vallentin in 2020 for bounding product-free sets in finite groups. We show that h(G) is an NP-hard parameter and, as a crucial ingredient, that it is NP-complete to decide whether a bipartite graph G has a balanced maximum independent set. These hardness results motivate introducing semidefinite programming (SDP) bounds for g(G), h(G), and αbal(G) (the maximum cardinality of a balanced independent set). We show that these bounds can be seen as natural variations of the Lovász ϑ-number, a well-known semidefinite bound on α(G). In addition, we formulate closed-form eigenvalue bounds, and we show relationships among them as well as with earlier spectral parameters by Hoffman and Haemers in 2001 and Vallentin in 2020
Optimizing mobile stroke unit deployment: A strategic case study in the greater Oslo area
Get PDFIntroduction: A Mobile Stroke Unit (MSU) enables prehospital acute stroke assessment, which leads to increased treatment rates and improved patient outcomes. However, for optimal utilization of the specialized resource, identifying the proper location for the MSU is crucial. Motivated by this, our goal was to find the optimal placement of an MSU in the greater Oslo area using geospatial mapping, and to explore how the location may influence acute stroke treatment. Methods: Historical data on suspected and confirmed strokes with the respective geospatial data and calculated travel times were analyzed using a mathematical optimization model based on the Maximum Coverage Location Problem (MCLP) and solved with the Gurobi solver. The model is universal and may be adapted to other regions and countries. Results: The optimal base location for a single MSU in the greater Oslo area would increase the coverage of stroke patients by 17%. The rendez-vous approach would further improve the coverage by approximately 300% for confirmed stroke patients. In the optimal location, the MSU has the potential to reduce time to thrombolysis by 27 minutes (25%) and time to thrombectomy by around 35 minutes (20%). Conclusion: Strategic placement of an MSU in the greater Oslo area significantly increases patient coverage and may reduce treatment times in acute stroke. Geospatial analyses have the potential to aid decision making on MSU location, optimize prehospital acute stroke assessment and improve patient outcomes
Macroscopic parameterization of positive streamer heads in air
No full textThe growth of streamer discharges is determined at their heads, for individual streamers as well as in collective phenomena, such as streamer trees or coronas or streamer bursts ahead of lightning leaders. Some properties of the streamer heads, such as velocity v and radius R now can be measured quite well, but this is very challenging for others such as the maximal electric field, the charge content of the streamer head and the degree of chemical excitation and ionization in the streamer channel. Here we develop, test and evaluate a macroscopic approximation for positive streamer heads in air that relates macroscopic streamer head properties to each other. In particular, we find that velocity v, radius R and background field Ebg determine the complete profile of streamer heads with photoionization, if they propagate steadily. We also review Naidis’ approximate relation between v, R and the maximal field Emax . The approximate head model developed in the present paper consists of three first-order ordinary differential equations along the streamer axis. It is derived from the classical fluid model for streamer discharges by assuming axisymmetry, steady streamer propagation (i.e. with constant velocity and shape), and a spherical shape of the charge layer around the streamer head. The new reduced model agrees well with full solutions of the classical fluid model, even when it is applied to accelerating streamers. Therefore the model can be used for evaluations of experiments, like for the determination of the maximal electric field from radius and velocity of the streamer. It is also a step towards constructing reduced models for the collective dynamics of multi-streamer discharges
Sample-path large deviations for unbounded additive functionals of the reflected random walk
Get PDFWe prove a sample-path large deviation principle (LDP) with sublinear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space D[0, 1] equipped with the M′1 topology. Our technique hinges on a suitable decomposition of the Markov chain in terms of regeneration cycles. Each regeneration cycle denotes the area accumulated during the busy period of the reflected random walk. We prove a large deviation principle for the area under the busy period of the Markov random walk, and we show that it exhibits a heavy-tailed behavior
PDX: A Data Layout for Vector Similarity Search
Get PDFWe propose Partition Dimensions Across (PDX), a data layout for vectors (e.g., embeddings) that, similar to PAX [6], stores multiple vectors in one block, using a vertical layout for the dimensions (Figure 1). PDX accelerates exact and approximate similarity search thanks to its dimension-by-dimension search strategy that operates on multiple-vectors-at-a-time in tight loops. It beats SIMD-optimized distance kernels on standard horizontal vector storage (avg 40% faster), only relying on scalar code that gets auto-vectorized. We combined the PDX layout with recent dimension-pruning algorithms ADSampling [19] and BSA [52] that accelerate approximate vector search. We found that these algorithms on the horizontal vector layout can lose to SIMD-optimized linear scans, even if they are SIMD-optimized. However, when used on PDX, their benefit is restored to 2-7x. We find that search on PDX is especially fast if a limited number of dimensions has to be scanned fully, which is what the dimension-pruning approaches do. We finally introduce PDX-BOND, an even more flexible dimension-pruning strategy, with good performance on exact search and reasonable performance on approximate search. Unlike previous pruning algorithms, it can work on vector data "as-is" without preprocessing; making it attractive for vector databases with frequent updates
Efficient Monte Carlo simulation of streamer discharges with deep-learning denoising models
Get PDFElectric breakdown in non-conducting gases is a complex process that in its first stages is characterized by filamentary discharges called streamers. Streamer dynamics are inherently nonlinear and span broad temporal and spatial scales, making numerical simulation challenging. Although Monte Carlo methods are intuitive and they model the full electron energy distribution without a priori prescriptions, they suffer from artificial sampling noise which, combined with the non-linearity of streamers, distorts their evolution. Here we investigate the use of deep-learning techniques to mitigate the noise introduced by Monte Carlo sampling. We observe that traditional techniques for noise reduction in images are not satisfactory because they do not impose strict conservation of electric charge. Then we present a charge-conserving denoising filter to improve the efficiency of Monte Carlo simulations of streamers
Mixed Schur-Weyl duality in quantum information
Get PDFThis thesis explores the interplay between representation theory and quantum information.
Specifically, we focus on mixed Schur–Weyl duality, which considers the action of the unitary group on mixed tensors.
This setting naturally arises in quantum information tasks involving unitary-equivariant channels, such as port-based teleportation, quantum majority vote, and universal transposition of unitary operators.
A key contribution of this thesis is an explicit derivation of the action of the generators of the partially transposed permutation matrix algebra—the commutant of the mixed unitary action—in the Gelfand–Tsetlin basis.
As another key result of this thesis, we develop efficient quantum circuits for the mixed quantum Schur transform, a novel primitive in quantum information.
The key ingredient of our construction is new efficient circuits for the dual Clebsch–Gordan transform of the unitary group.
A significant application of our findings is the construction of efficient quantum algorithms for port-based teleportation, a variant of quantum teleportation that eliminates the need for corrective operations.
Another application is a symmetry reduction of semidefinite optimisation problems with unitary equivariance symmetry.
Finally, we study the extendibility of quantum states possessing unitary, mixed unitary, or orthogonal symmetry on the complete graph.
We obtain analytically the exact maximum values for projections onto the maximally entangled state and the antisymmetric state for each of the three symmetry classes.
This thesis demonstrates the usefulness of mixed Schur–Weyl duality in quantum information and computing.
We expect that our tools will help address other problems in other areas of quantum information processing, such as communication, cryptography, and simulation
Whale - Shoe - Bottle
No full textIs it a shoe? A bottle? Or, a whale? As it turns out, all three: a bottle in the shape of a shoe in the shape of a whale. The exact use of this rather peculiar object remains an intriguing question. Was it actually used as a bottle, or is the removable tail-shaped cork merely decorative? Was it perhaps made by a shoemaker as a masters test before they were allowed to enter the cobbler’s guild? Explore the 3D visualization of this peculiar object from the Rijksmuseum collection (on loan from the Koninklijk Oudheidkundig Genootschap (KOG)) to look at this object up close and discover the research that has been performed on it using CT scanning and 3D scanning