722 results on '"P. Luczak"'
Search Results
2. Confidence is detection-like in high-dimensional spaces
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Łuczak, Wiktoria, O'Neill, Kevin, and Fleming, Stephen M.
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Quantitative Biology - Neurons and Cognition - Abstract
Confidence estimates are often "detection-like" - driven by positive evidence in favour of a decision. This empirical observation has been interpreted as showing human metacognition is limited by biases or heuristics. Here we show that Bayesian confidence estimates also exhibit heightened sensitivity to decision-congruent evidence in higher-dimensional signal detection theoretic spaces, leading to detection-like confidence criteria. This effect is due to a nonlinearity induced by normalisation of confidence by a large number of unchosen alternatives. Our analysis suggests that detection-like confidence is rational when computing confidence in a higher-dimensional evidence space than that assumed by the experimenter.
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- 2024
3. Cutoff for the logistic SIS epidemic model with self-infection
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He, Roxanne, Luczak, Malwina, and Ross, Nathan
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Mathematics - Probability - Abstract
We study a variant of the classical Markovian logistic SIS epidemic model on a complete graph, which has the additional feature that healthy individuals can become infected without contacting an infected member of the population. This additional ``self-infection'' is used to model situations where there is an unknown source of infection or an external disease reservoir, such as an animal carrier population. In contrast to the classical logistic SIS epidemic model, the version with self-infection has a non-degenerate stationary distribution, and we show that it exhibits the cutoff phenomenon, which is a sharp transition in time from one to zero of the total variation distance to stationarity. While this result is interesting in its own right, an additional contribution of our work is that the proof illustrates a recently formalised methodology of Barbour, Brightwell and Luczak, which can be used to show cutoff via a combination of concentration of measure inequalities and coupling techniques., Comment: 26 pages
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- 2024
4. Strong Brandt-Thomass\'e Theorems
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Łuczak, Tomasz, Polcyn, Joanna, and Reiher, Christian
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Mathematics - Combinatorics ,05C35, 05C07, 05C15 - Abstract
Solving a long standing conjecture of Erd\H{o}s and Simonovits, Brandt and Thomass\'e proved that the chromatic number of each triangle-free graph $G$ such that $\delta(G)>|V(G)|/3$ is at most four. In fact, they showed the much stronger result that every maximal triangle-free graph $G$ satisfying this minimum degree condition is a blow-up of either an Andr\'asfai or a Vega graph. Here we establish the same structural conclusion on $G$ under the weaker assumption that for $m\in\{2, 3, 4\}$ every sequence of $3m$ vertices has a subsequence of length $m+1$ with a common neighbour. In forthcoming work this will be used to solve an old problem of Andr\'asfai in Ramsey-Tur\'an theory., Comment: 34 figures
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- 2024
5. On Segal entropy
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Łuczak, Andrzej
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Mathematics - Operator Algebras ,46L53 (Primary), 81P45, 62B15 (Secondary) - Abstract
The paper is devoted to the investigation of Segal's entropy in semifinite von Neumann algebras. The following questions are dealt with: semicontinuity, the 'ideal-like' structure of the linear span of the set of operators with finite entropy, and topological properties of the set of operators with finite as well as infinite entropy. In our analysis, full generality is aimed at, in particular, the operators for which the entropy is considered are not assumed to belong to the underlying von Neumann algebra, instead, they are arbitrary positive elements in the space $L^1$ over the algebra.
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- 2024
6. Organization of a functional glycolytic metabolon on mitochondria for metabolic efficiency
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Wang, Haoming, Vant, John W., Zhang, Andrew, Sanchez, Richard G., Wu, Youjun, Micou, Mary L., Luczak, Vincent, Whiddon, Zachary, Carlson, Natasha M., Yu, Seungyoon B., Jabbo, Mirna, Yoon, Seokjun, Abushawish, Ahmed A., Ghassemian, Majid, Masubuchi, Takeya, Gan, Quan, Watanabe, Shigeki, Griffis, Eric R., Hammarlund, Marc, Singharoy, Abhishek, and Pekkurnaz, Gulcin
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- 2024
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7. On the linkage of momentum and reversal – evidence from the G7 stock markets
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Hofmann, Daniel, Keiber, Karl Ludwig, and Luczak, Adalbert
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- 2024
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8. Tracking changes in functionality and morphology of repopulated microglia in young and old mice
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Luczak-Sobotkowska, Zuzanna M., Rosa, Patrycja, Lopez, Maria Banqueri, Ochocka, Natalia, Kiryk, Anna, Lenkiewicz, Anna M., Furhmann, Martin, Jankowski, Aleksander, and Kaminska, Bozena
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- 2024
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9. Associating sensory cues with incoming seizures: developing an animal model of auras
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Das, Ritwik, Howey, Carlos, McFetridge, Autumn, Lapointe, Valérie, and Luczak, Artur
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- 2024
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10. A novel theta-controlled vibrotactile brain–computer interface to treat chronic pain: a pilot study
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Demarest, Phillip, Rustamov, Nabi, Swift, James, Xie, Tao, Adamek, Markus, Cho, Hohyun, Wilson, Elizabeth, Han, Zhuangyu, Belsten, Alexander, Luczak, Nicholas, Brunner, Peter, Haroutounian, Simon, and Leuthardt, Eric C.
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- 2024
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11. Tracking changes in functionality and morphology of repopulated microglia in young and old mice
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Zuzanna M. Luczak-Sobotkowska, Patrycja Rosa, Maria Banqueri Lopez, Natalia Ochocka, Anna Kiryk, Anna M. Lenkiewicz, Martin Furhmann, Aleksander Jankowski, and Bozena Kaminska
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Microglial heterogeneity ,CSF1R inhibitors ,Microglia repopulation ,ScRNA-seq ,Transcriptomics ,Aging ,Neurology. Diseases of the nervous system ,RC346-429 - Abstract
Abstract Background Microglia (MG) are myeloid cells of the central nervous system that support homeostasis and instigate neuroinflammation in pathologies. Single-cell RNA sequencing (scRNA-seq) revealed the functional heterogeneity of MG in mouse brains. Microglia are self-renewing cells and inhibition of colony-stimulating factor 1 receptor (CSF1R) signaling depletes microglia which rapidly repopulate. The functions of repopulated microglia are poorly known. Methods We combined scRNA-seq, bulk RNA-seq, immunofluorescence, and confocal imaging to study the functionalities and morphology of repopulated microglia. Results A CSRF1R inhibitor (BLZ-945) depleted microglia within 21 days and a number of microglia was fully restored within 7 days, as confirmed by TMEM119 staining and flow cytometry. ScRNA-seq and computational analyses demonstrate that repopulated microglia originated from preexisting progenitors and reconstituted functional clusters but upregulated inflammatory genes. Percentages of proliferating, immature microglia displaying inflammatory gene expression increased in aging mice. Morphometric analysis of MG cell body and branching revealed a distinct morphology of repopulated MG, particularly in brains of old mice. We demonstrate that with aging some repopulated MG fail to reach the homeostatic phenotype. These differences may contribute to the deterioration of MG protective functions with age.
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- 2024
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12. On size Ramsey numbers for a pair of cycles
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Bednarska-Bzdęga, Małgorzata and Łuczak, Tomasz
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Mathematics - Combinatorics ,05C55 (Primary), 05C38 (Secondary) - Abstract
We show that there exists an absolute constant $A$ such that the size Ramsey number of a pair of cycles $(C_n$, $C_{2d})$, where $4\le 2d\le n$, is bounded from above by $An$. We also study the restricted size Ramsey number for such a pair., Comment: 14 pages
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- 2023
13. The next case of Andr\'asfai's conjecture
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Łuczak, Tomasz, Polcyn, Joanna, and Reiher, Christian
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Mathematics - Combinatorics ,05C35, 05C69 - Abstract
Let $\mathrm{ex}(n,s)$ denote the maximum number of edges in a triangle-free graph on $n$ vertices which contains no independent sets larger than $s$. The behaviour of $\mathrm{ex}(n,s)$ was first studied by Andr\'asfai, who conjectured that for $s>n/3$ this function is determined by appropriately chosen blow-ups of so called Andr\'asfai graphs. Moreover, he proved $\mathrm{ex}(n, s)=n^2-4ns+5s^2$ for $s/n\in [2/5, 1/2]$ and in earlier work we obtained $\mathrm{ex}(n, s)=3n^2-15ns+20s^2$ for $s/n\in [3/8, 2/5]$. Here we make the next step in the quest to settle Andr\'asfai's conjecture by proving $\mathrm{ex}(n, s)=6n^2-32ns+44s^2$ for $s/n\in [4/11, 3/8]$., Comment: Dedicated to the memory of Vera T. S\'os
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- 2023
14. A Note on the Markovian SIR Epidemic on a Random Graph with Given Degrees
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Luczak, Malwina
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- 2024
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15. State of the art and future research directions of materials science applied to electrochemical biosensor developments
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Kny, Erich, Hasler, Roger, Luczak, Wiktor, Knoll, Wolfgang, Szunerits, Sabine, and Kleber, Christoph
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- 2024
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16. Edge Devices Inference Performance Comparison
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Tobiasz, R., Wilczyński, G., Graszka, P., Czechowski, N., and Łuczak, S.
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Computer Science - Machine Learning ,Computer Science - Computer Vision and Pattern Recognition ,I.2.10 ,B.8.0 - Abstract
In this work, we investigate the inference time of the MobileNet family, EfficientNet V1 and V2 family, VGG models, Resnet family, and InceptionV3 on four edge platforms. Specifically NVIDIA Jetson Nano, Intel Neural Stick, Google Coral USB Dongle, and Google Coral PCIe. Our main contribution is a thorough analysis of the aforementioned models in multiple settings, especially as a function of input size, the presence of the classification head, its size, and the scale of the model. Since throughout the industry, those architectures are mainly utilized as feature extractors we put our main focus on analyzing them as such. We show that Google platforms offer the fastest average inference time, especially for newer models like MobileNet or EfficientNet family, while Intel Neural Stick is the most universal accelerator allowing to run most architectures. These results should provide guidance for engineers in the early stages of AI edge systems development. All of them are accessible at https://bulletprove.com/research/edge_inference_results.csv
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- 2023
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17. Human-centric Literature on Trust for SfTI Veracity Spearhead
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Blincoe, Kelly, Luczak-Roesch, Markus, Miller, Tim, and Galster, Matthias
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Computer Science - Computers and Society ,Computer Science - Software Engineering - Abstract
This article summarizes the literature on trust of digital technologies from a human-centric perspective. We summarize literature on trust in face-to-face interactions from other fields, followed by a discussion of organizational trust, technology-mediated trust, trust of software products, trust of AI, and blockchain. This report was created for the Science for Technological Innovation Veracity Spearhead supported by New Zealand's National Science Challenges.
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- 2023
18. A Nonparametric, Mixed Effect, Maximum Likelihood Estimator for the Distribution of Random Parameters in Discrete-Time Abstract Parabolic Systems with Application to the Transdermal Transport of Alcohol
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Asserian, Lernik, Luczak, Susan E., and Rosen, I. G.
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Statistics - Methodology ,Mathematics - Optimization and Control - Abstract
The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems are established by taking a nonparametric approach in the context of a mixed effects statistical model using a Prohorov metric framework on a set of feasible measures. A theoretical convergence result for a finite dimensional approximation scheme for computing the maximum likelihood estimator is also established and the efficacy of the approach is demonstrated by applying the scheme to the transdermal transport of alcohol modeled by a random parabolic PDE. Numerical studies included show that the maximum likelihood estimator is statistically consistent in that the convergence of the estimated distribution to the "true" distribution is observed in an example involving simulated data. The algorithm developed is then applied to two datasets collected using two different transdermal alcohol biosensors. Using the leave-one-out cross-validation method, we get an estimate for the distribution of the random parameters based on a training set. The input from a test drinking episode is then used to quantify the uncertainty propagated from the random parameters to the output of the model in the form of a 95% error band surrounding the estimated output signal., Comment: arXiv admin note: text overlap with arXiv:2304.11806
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- 2023
19. Prohorov Metric-Based Nonparametric Estimation of the Distribution of Random Parameters in Abstract Parabolic Systems with Application to the Transdermal Transport of Alcohol
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Asserian, Lernik, Luczak, Suzan E., and Rosen, I. G.
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Statistics - Methodology ,Mathematics - Optimization and Control - Abstract
We consider a Prohorov metric-based nonparametric approach to estimating the probability distribution of a random parameter vector in discrete-time abstract parabolic systems. We establish the existence and consistency of a least squares estimator. We develop a finite-dimensional approximation and convergence theory, and obtain numerical results by applying the nonparametric estimation approach and the finite-dimensional approximation framework to a problem involving an alcohol biosensor, wherein we estimate the probability distribution of random parameters in a parabolic PDE. To show the convergence of the estimated distribution to the "true" distribution, we simulate data from the "true" distribution, apply our algorithm, and obtain the estimated cumulative distribution function. We then use the Markov Chain Monte Carlo Metropolis Algorithm to generate random samples from the estimated distribution, and perform a generalized (2-dimensional) two-sample Kolmogorov-Smirnov test with null hypothesis that our generated random samples from the estimated distribution and generated random samples from the "true" distribution are drawn from the same distribution. We then apply our algorithm to actual human subject data from the alcohol biosensor and observe the behavior of the normalized root-mean-square error (NRMSE) using leave-one-out cross-validation (LOOCV) under different model complexities.
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- 2023
20. What does ChatGPT return about human values? Exploring value bias in ChatGPT using a descriptive value theory
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Fischer, Ronald, Luczak-Roesch, Markus, and Karl, Johannes A
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Computer Science - Computation and Language ,Computer Science - Computers and Society ,Computer Science - Human-Computer Interaction ,68T50 - Abstract
There has been concern about ideological basis and possible discrimination in text generated by Large Language Models (LLMs). We test possible value biases in ChatGPT using a psychological value theory. We designed a simple experiment in which we used a number of different probes derived from the Schwartz basic value theory (items from the revised Portrait Value Questionnaire, the value type definitions, value names). We prompted ChatGPT via the OpenAI API repeatedly to generate text and then analyzed the generated corpus for value content with a theory-driven value dictionary using a bag of words approach. Overall, we found little evidence of explicit value bias. The results showed sufficient construct and discriminant validity for the generated text in line with the theoretical predictions of the psychological model, which suggests that the value content was carried through into the outputs with high fidelity. We saw some merging of socially oriented values, which may suggest that these values are less clearly differentiated at a linguistic level or alternatively, this mixing may reflect underlying universal human motivations. We outline some possible applications of our findings for both applications of ChatGPT for corporate usage and policy making as well as future research avenues. We also highlight possible implications of this relatively high-fidelity replication of motivational content using a linguistic model for the theorizing about human values., Comment: 26 pages, 4 Figures, 5 Tables
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- 2023
21. Associating sensory cues with incoming seizures: developing an animal model of auras
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Ritwik Das, Carlos Howey, Autumn McFetridge, Valérie Lapointe, and Artur Luczak
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Medicine ,Science - Abstract
Abstract For patients with epilepsy, one of the biggest problems is the unpredictability of the time when the next seizure will occur. Interestingly, some epileptic patients experience a sensory sensation preceding seizures, called aura, which helps them move to safety before a seizure. Here, we describe the development of the first animal model of auras, which could allow for a more detailed study of this phenomenon. Specifically, in mice, we presented sensory stimuli (sound and light cues) a few seconds before kindling an animal to induce seizures. Animals were kindled by electrical stimulation in the basolateral amygdalar nucleus. Over the course of stimulation sessions, animals started showing progressively stronger freezing behavior to sensory cues preceding kindling. Interestingly, seizures are known to cause retrograde amnesia, thus it was surprising that the association between seizures and preceding sensory cues developed in all experimental animals. In summary, our experiments show that similarly to auras, a sensory sensation can be associated with incoming generalized seizures and is not erased by retrograde amnesia.
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- 2024
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22. Mappings preserving quantum Renyi's entropies in von Neumann algebras
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Łuczak, Andrzej, Podsędkowska, Hanna, and Wieczorek, Rafał
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Mathematics - Operator Algebras ,Mathematical Physics ,Mathematics - Functional Analysis ,Mathematics - Quantum Algebra ,Quantum Physics - Abstract
We investigate the situation when a normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change fixed quantum Renyi's entropy of the density of a normal state. It is also shown that such a map does not change the entropy of any density if and only if it is a Jordan *-isomorphism on the algebra.
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- 2023
23. LOPES 3D -- studies on the benefits of EAS-radio measurements with vertically aligned antennas
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Huber, D., Apel, W. D., Arteaga-Velazquez, J. C., Bähren, L., Bekk, K., Bertaina, M., Biermann, P. L., Blümer, J., Bozdog, H., Brancus, I. M., Cantoni, E., Chiavassa, A., Daumiller, K., de Souza, V., Di Pierro, F., Doll, P., Engel, R., Falcke, H., Fuchs, B., Fuhrmann, D., Gemmeke, H., Grupen, C., Haungs, A., Heck, D., Hörandel, J. R., Horneffer, A., Huege, T., Isar, P. G., Kampert, K. -H., Kang, D., Krömer, O., Kuijpers, J., Link, K., Łuczak, P., Ludwig, M., Mathes, H. J., Melissas, M., Morello, C., Oehlschläger, J., Palmieri, N., Pierog, T., Rautenberg, J., Rebel, H., Roth, M., Rühle, C., Saftoiu, A., Schieler, H., Schmidt, A., Schoo, S., Schröder, F. G., Sima, O., Toma, G., Trinchero, G. C., Weindl, A., Wochele, J., Zabierowski, J., and Zensus, J. A.
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Astrophysics - Instrumentation and Methods for Astrophysics ,Astrophysics - High Energy Astrophysical Phenomena - Abstract
The LOPES experiment was a radio interferometer built at the existing air shower array KASCADE-Grande in Karlsruhe, Germany. The last configuration of LOPES was called LOPES 3D and consisted of ten tripole antennas. Each of these antennas consisted of three crossed dipoles east-west, north-south, and vertically aligned. With this, LOPES 3D had the unique possibility to study the benefits of measurements with vertically aligned antennas in the environment of the well understood and calibrated particle detector array KASCADE-Grande. The measurements with three spatially coincident antennas allows a redundant reconstruction of the electric field vector. Several methods to exploit the redundancy were developed and tested. Furthermore, for the first time in LOPES, the background noise could be studied polarization- and direction dependent. With LOPES 3D it could be demonstrated that radio detection reaches a higher efficiency for inclined showers when including measurements with vertically aligned antennas and that the vertical component gets more important for the measurement of inclined showers. In this contribution we discuss a weighting scheme for the best combination of three redundant reconstructed electric field vectors. Furthermore, we discuss the influence of these weighting schemes on the ability to reconstruct air showers using the radio method. We show an estimate of the radio efficiency for inclined showers with focus on the benefits of measurements with vertically aligned antennas and we present the direction dependent noise in the different polarizations., Comment: Submission to the proceedings of the ARENA2014 workshop, which unfortunately were never published; thus documented here for reference
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- 2022
24. On the restricted size Ramsey number for a pair of cycles
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Łuczak, Tomasz, Polcyn, Joanna, and Rahimi, Zahra
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Mathematics - Combinatorics ,Primary: 05D10, secondary: 05C38, 05C55 - Abstract
For graphs $H_1,H_2$ by $r^*(H_1,H_2)$ we denote the minimum number of edges in a graph $G$ on $r(H_1,H_2)$ vertices such that $G\to (H_1,H_2)$. We show that for each pair of natural numbers $k,n$, $k\le n$, where $k$ is odd and $n$ is large enough, we have $$r^*(C_n,C_k)=\lceil (n+1)(2n-1)/2\rceil \,.$$
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- 2022
25. Non-daily Cigarette Smoking: Stability and Transition to Abstinence in Young Adults
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Doran, Neal, Myers, Mark, Luczak, Susan, Trim, Ryan, Strong, David, and Tully, Lyric
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Epidemiology ,Public Health ,Health Sciences ,Tobacco ,Clinical Research ,Tobacco Smoke and Health ,Prevention ,Behavioral and Social Science ,3.1 Primary prevention interventions to modify behaviours or promote wellbeing ,Cancer ,Good Health and Well Being ,Young Adult ,Male ,Humans ,Adult ,Adolescent ,Female ,Cigarette Smoking ,Electronic Nicotine Delivery Systems ,Smoking Cessation ,Smokers ,Tobacco Products ,Clinical Sciences ,Public Health and Health Services ,Marketing ,Public health - Abstract
IntroductionThere is increasing recognition that non-daily cigarette smoking is common in early adulthood but less is known about its stability over time, or what influences transitions to heavier or nonsmoking. We examined the stability of non-daily smoking in a sample of young adults, and tested whether social and cognitive factors predicted transitions to other smoking patterns over time.Aims and methodsParticipants were 579 young adults (18-24 years old at enrollment, 52% male) who were non-daily and never-daily cigarette smokers and California residents. Participants completed 13 waves of assessment over 3 years. We used descriptive statistics to evaluate the frequency of consistent abstinence, defined as no cigarette use at two consecutive waves and no cigarette use at any subsequent waves. Cox and logistic regression were used to test predictors of consistent abstinence.ResultsWe found that 55% of participants smoked intermittently throughout the study, while 43% were consistently abstinent by the end of the study; few transitioned to daily smoking. Stopping smoking was associated with having fewer smoking friends, smoking less in social situations, having lower positive reinforcement expectancies for smoking, and having stronger intent to quit. Post hoc analyses indicated those who stopped smoking tended to report reductions in positive reinforcement expectancies and increased intent to quit in the 6 months before stopping.ConclusionsFindings suggest a substantial minority of young adult non-daily smokers may stop on their own, but that the majority continue smoking and may require intervention. Interventions for this population should address social motives and reinforcement expectancies.ImplicationsThe majority of young adults who are non-daily cigarette smokers appear to maintain this habit over an extended period and may require intervention. Interventions that focus on reducing expectancies for positive effects of and social motives for cigarette use and on increasing intent to quit smoking may be most effective.
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- 2023
26. Chondroprotection of articular cartilage integrity: Utilizing ultrasonic scalpel and hyperosmolar irrigation solution during cutting
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Nisreen Mohammed Al-Namnam, Aneta T. Luczak, Irene Yang, Xuan Li, Margaret Lucas, Andrew C. Hall, and A. Hamish R.W. Simpson
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Ultrasonic cutting ,Articular cartilage ,Chondroprotection ,Osmolarity ,Diseases of the musculoskeletal system ,RC925-935 - Abstract
Objectives: Ultrasonic (US) cutting of cartilage in orthopaedic surgery has received little attention despite its potential to reduce chondrocyte death which could enhance cartilage repair. We aimed to investigate whether an ultrasonically-vibrating scalpel to cut human articular cartilage could reduce chondrocyte death, and to determine if hyper-osmolarity could provide chondroprotection during the procedure. Methods: A scalpel (no. 15) was mounted on an ultrasonic transducer to resonate at 35 kHz with 30 μm vibrational displacement. Thirty-six fresh human femoral cartilage samples were divided into four groups based on ultrasonic activation (US or non-US) and saline osmolarity (300 or 600 mOsm/L). Cell viability was assessed using a live/dead cell assay and analysed quantitatively by confocal microscopy. Histology illustrated tissue surface changes at the cut site. Results: The overall chondrocyte death percentage at both the US and non-US cut sites showed comparable results (p > 0.05) in both osmolarities. However, the zone of chondrocyte death was reduced by 31 ± 5% and 36 ± 6%, respectively, when comparing US cutting at 300 mOsm/L and 600 mOsm/L to the control group (non-US cutting; 300 mOsm/L) (p
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- 2024
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27. Hippocluster: an efficient, hippocampus-inspired algorithm for graph clustering
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Chalmers, Eric and Luczak, Artur
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Condensed Matter - Disordered Systems and Neural Networks ,Computer Science - Neural and Evolutionary Computing ,I.5.3 - Abstract
Random walks can reveal communities or clusters in networks, because they are more likely to stay within a cluster than leave it. Thus, one family of community detection algorithms uses random walks to measure distance between pairs of nodes in various ways, and then applies K-Means or other generic clustering methods to these distances. Interestingly, information processing in the brain may suggest a simpler method of learning clusters directly from random walks. Drawing inspiration from the hippocampus, we describe a simple two-layer neural learning framework. Neurons in one layer are associated with graph nodes and simulate random walks. These simulations cause neurons in the second layer to become tuned to graph clusters through simple associative learning. We show that if these neuronal interactions are modelled a particular way, the system is essentially a variant of K-Means clustering applied directly in the walk-space, bypassing the usual step of computing node distances/similarities. The result is an efficient graph clustering method. Biological information processing systems are known for high efficiency and adaptability. In tests on benchmark graphs, our framework demonstrates this high data-efficiency, low memory use, low complexity, and real-time adaptation to graph changes, while still achieving clustering quality comparable to other algorithms., Comment: 10 pages, 8 figures
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- 2022
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28. Reinforcement Learning with Brain-Inspired Modulation can Improve Adaptation to Environmental Changes
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Chalmers, Eric and Luczak, Artur
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Computer Science - Artificial Intelligence ,I.2.6 - Abstract
Developments in reinforcement learning (RL) have allowed algorithms to achieve impressive performance in highly complex, but largely static problems. In contrast, biological learning seems to value efficiency of adaptation to a constantly-changing world. Here we build on a recently-proposed neuronal learning rule that assumes each neuron can optimize its energy balance by predicting its own future activity. That assumption leads to a neuronal learning rule that uses presynaptic input to modulate prediction error. We argue that an analogous RL rule would use action probability to modulate reward prediction error. This modulation makes the agent more sensitive to negative experiences, and more careful in forming preferences. We embed the proposed rule in both tabular and deep-Q-network RL algorithms, and find that it outperforms conventional algorithms in simple, but highly-dynamic tasks. We suggest that the new rule encapsulates a core principle of biological intelligence; an important component for allowing algorithms to adapt to change in a human-like way., Comment: 9 pages, 5 figures
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- 2022
29. Biologically-inspired neuronal adaptation improves learning in neural networks
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Kubo, Yoshimasa, Chalmers, Eric, and Luczak, Artur
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Computer Science - Neural and Evolutionary Computing ,Computer Science - Artificial Intelligence ,Computer Science - Machine Learning - Abstract
Since humans still outperform artificial neural networks on many tasks, drawing inspiration from the brain may help to improve current machine learning algorithms. Contrastive Hebbian Learning (CHL) and Equilibrium Propagation (EP) are biologically plausible algorithms that update weights using only local information (without explicitly calculating gradients) and still achieve performance comparable to conventional backpropagation. In this study, we augmented CHL and EP with Adjusted Adaptation, inspired by the adaptation effect observed in neurons, in which a neuron's response to a given stimulus is adjusted after a short time. We add this adaptation feature to multilayer perceptrons and convolutional neural networks trained on MNIST and CIFAR-10. Surprisingly, adaptation improved the performance of these networks. We discuss the biological inspiration for this idea and investigate why Neuronal Adaptation could be an important brain mechanism to improve the stability and accuracy of learning., Comment: 17 pages
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- 2022
30. A novel theta-controlled vibrotactile brain–computer interface to treat chronic pain: a pilot study
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Phillip Demarest, Nabi Rustamov, James Swift, Tao Xie, Markus Adamek, Hohyun Cho, Elizabeth Wilson, Zhuangyu Han, Alexander Belsten, Nicholas Luczak, Peter Brunner, Simon Haroutounian, and Eric C. Leuthardt
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Medicine ,Science - Abstract
Abstract Limitations in chronic pain therapies necessitate novel interventions that are effective, accessible, and safe. Brain–computer interfaces (BCIs) provide a promising modality for targeting neuropathology underlying chronic pain by converting recorded neural activity into perceivable outputs. Recent evidence suggests that increased frontal theta power (4–7 Hz) reflects pain relief from chronic and acute pain. Further studies have suggested that vibrotactile stimulation decreases pain intensity in experimental and clinical models. This longitudinal, non-randomized, open-label pilot study's objective was to reinforce frontal theta activity in six patients with chronic upper extremity pain using a novel vibrotactile neurofeedback BCI system. Patients increased their BCI performance, reflecting thought-driven control of neurofeedback, and showed a significant decrease in pain severity (1.29 ± 0.25 MAD, p = 0.03, q = 0.05) and pain interference (1.79 ± 1.10 MAD p = 0.03, q = 0.05) scores without any adverse events. Pain relief significantly correlated with frontal theta modulation. These findings highlight the potential of BCI-mediated cortico-sensory coupling of frontal theta with vibrotactile stimulation for alleviating chronic pain.
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- 2024
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31. Continuous harmonic functions on a ball that are not in $H^s$ for $s>1/2$
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Bramati, Roberto, Riva, Matteo Dalla, and Luczak, Brian
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Mathematics - Analysis of PDEs ,Mathematics - Classical Analysis and ODEs ,Mathematics - Functional Analysis ,31A20, 31B25, 33C55, 35A09, 35B65, 35G30, 42B37, 46E35 - Abstract
We show that there are harmonic functions on a ball ${\mathbb{B}_n}$ of $\mathbb{R}^n$, $n\ge 2$, that are continuous up to the boundary (and even H\"older continuous) but not in the Sobolev space $H^s(\mathbb{B}_n)$ for any $s$ sufficiently big. The idea for the construction of these functions is inspired by the two-dimensional example of a harmonic continuous function with infinite energy presented by Hadamard in 1906. To obtain examples in any dimension $n\ge 2$ we exploit certain series of spherical harmonics. As an application, we verify that the regularity of the solutions that was proven for a class of boundary value problems with nonlinear transmission conditions is, in a sense, optimal., Comment: 19 pages
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- 2022
32. Entropy of Neuronal Spike Patterns
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Artur Luczak
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information theory ,neuronal analyses ,spike train entropy ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
Neuronal spike patterns are the fundamental units of neural communication in the brain, which is still not fully understood. Entropy measures offer a quantitative framework to assess the variability and information content of these spike patterns. By quantifying the uncertainty and informational content of neuronal patterns, entropy measures provide insights into neural coding strategies, synaptic plasticity, network dynamics, and cognitive processes. Here, we review basic entropy metrics and then we provide examples of recent advancements in using entropy as a tool to improve our understanding of neuronal processing. It focuses especially on studies on critical dynamics in neural networks and the relation of entropy to predictive coding and cortical communication. We highlight the necessity of expanding entropy measures from single neurons to encompass multi-neuronal activity patterns, as cortical circuits communicate through coordinated spatiotemporal activity patterns, called neuronal packets. We discuss how the sequential and partially stereotypical nature of neuronal packets influences the entropy of cortical communication. Stereotypy reduces entropy by enhancing reliability and predictability in neural signaling, while variability within packets increases entropy, allowing for greater information capacity. This balance between stereotypy and variability supports both robustness and flexibility in cortical information processing. We also review challenges in applying entropy to analyze such spatiotemporal neuronal spike patterns, notably, the “curse of dimensionality” in estimating entropy for high-dimensional neuronal data. Finally, we discuss strategies to overcome these challenges, including dimensionality reduction techniques, advanced entropy estimators, sparse coding schemes, and the integration of machine learning approaches. Thus, this work summarizes the most recent developments on how entropy measures contribute to our understanding of principles underlying neural coding.
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- 2024
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33. Mathematical Modeling: A Study of Multidisciplinary Benefits in the Math Classroom
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Luczak, Richard and Erwin, Rob
- Abstract
Math modeling is a unique and powerful part of mathematics that is underutilized in contemporary classrooms. Teachers of all grade levels may utilize such modeling problems to better serve the students in their classrooms, with related analytical problem-solving activities that contribute to learners meeting the highest of learning standards. With a continued focus within mathematics education on critical thinking, creativity, disciplinary literacy and college/career readiness, math modeling is at the forefront of research-tested methods to develop these crucial skills. This is an important direction mathematics education that needs to go in order to prepare students for the future.
- Published
- 2023
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34. A niche‐based theory of island biogeography
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Gregory Beaugrand, Loick Kléparski, Christophe Luczak, Eric Goberville, and Richard R. Kirby
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area ,biodiversity ,island biogeography ,niche theory ,Ecology ,QH540-549.5 - Abstract
Abstract The equilibrium theory of island biogeography (ETIB) is a widely applied dynamic theory proposed in the 1960s to explain why islands have coherent differences in species richness. The development of the ETIB was temporarily challenged in the 1970s by the alternative static theory of ecological impoverishment (TEI). The TEI suggests that the number of species on an island is determined by its number of habitats or niches but, with no clear evidence relating species richness to the number of niches however, the TEI has been almost dismissed as a theory in favour of the original ETIB. Here, we show that the number of climatic niches on islands is an important predictor of the species richness of plants, herpetofauna and land birds. We therefore propose a model called the niche‐based theory of island biogeography (NTIB), based on the MacroEcological Theory on the Arrangement of Life (METAL), which successfully integrates the number of niches sensu Hutchinson into ETIB. To account for greater species turnover at the beginning of colonisation, we include higher initial extinction rates. When we test our NTIB for resident land birds in the Krakatau Islands, it reveals a good correspondence with observed species richness, immigration and extinction rates. Provided the environmental regime remains unchanged, we estimate that the current species richness at equilibrium is ~45 species (range between 38.39 and 61.51). Our NTIB provides better prediction because it counts for changes in species richness with latitude, which is not considered in any theory of island biogeography.
- Published
- 2024
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35. Results from the KASCADE-Grande Data Analysis
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Kang, D., Apel, W. D., Arteaga-Velázquez, J. C., Bekk, K., Bertaina, M., Blümer, J., Bozdog, H., Cantoni, E., Chiavassa, A., Cossavella, F., Daumiller, K., de Souza, V., Di Pierro, F., Doll, P., Engel, R., Fuhrmann, D., Gherghel-Lascu, A., Gils, H. J., Glasstetter, R., Grupen, C., Haungs, A., Heck, D., Hörandel, J. R., Huege, T., Kampert, K. -H., Klages, H. O., Link, K., Łuczak, P., Mathes, H. J., Mayer, H. J., Milke, J., Morello, C., Oehlschläger, J., Ostapchenko, S., Pierog, T., Rebel, H., Rivera-Rangel, D., Roth, M., Schieler, H., Schoo, S., Schröder, F. G., Sima, O., Toma, G., Trinchero, G. C., Ulrich, H., Weindl, A., Wochele, J., and Zabierowski, J.
- Subjects
Astrophysics - High Energy Astrophysical Phenomena - Abstract
KASCADE-Grande and its original array of KASCADE were dedicated to measure individual air showers of cosmic rays with great detail in the primary energy range of 100 TeV up to 1 EeV. The experiment has significantly contributed to investigations of the energy spectrum and chemical composition of cosmic rays in the transition region from galactic to extragalactic origin of cosmic rays as well as to the further development of hadronic interaction models through validity tests using the multi-detector information from KASCADE-Grande. Though the data accumulation was completed in 2013, the data analysis is still continuing. Recently, we investigate the reliability of the new hadronic interactions model of the Sibyll version 2.3d with the combined data from KASCADE and KASCADE-Grande, and compare it to the predictions of different hadronic interaction models. In addition, we update the web-based platform of the KASCADE Cosmic Ray Data Centre (KCDC), where now full datasets from KASCADE and KASCADE-Grande and the corresponding Monte-Carlo simulated events are available., Comment: Presented at the 37th International Cosmic Ray Conference (ICRC 2021)
- Published
- 2021
36. Computation of nonparametric, mixed effects, maximum likelihood, biosensor data based-estimators for the distributions of random parameters in an abstract parabolic model for the transdermal transport of alcohol
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Lernik Asserian, Susan E. Luczak, and I. G. Rosen
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nonparametric estimation ,mixed effects model ,maximum likelihood estimation ,existence and consistency ,random discrete-time dynamical systems ,random partial differential equations ,finite dimensional approximation and convergence ,alcohol biosensor ,transdermal alcohol concentration ,Biotechnology ,TP248.13-248.65 ,Mathematics ,QA1-939 - Abstract
The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems was established by taking a nonparametric approach in the context of a mixed effects statistical model using a Prohorov metric framework on a set of feasible measures. A theoretical convergence result for a finite dimensional approximation scheme for computing the maximum likelihood estimator was also established and the efficacy of the approach was demonstrated by applying the scheme to the transdermal transport of alcohol modeled by a random parabolic partial differential equation (PDE). Numerical studies included show that the maximum likelihood estimator is statistically consistent, demonstrated by the convergence of the estimated distribution to the "true" distribution in an example involving simulated data. The algorithm developed was then applied to two datasets collected using two different transdermal alcohol biosensors. Using the leave-one-out cross-validation (LOOCV) method, we found an estimate for the distribution of the random parameters based on a training set. The input from a test drinking episode was then used to quantify the uncertainty propagated from the random parameters to the output of the model in the form of a 95 error band surrounding the estimated output signal.
- Published
- 2023
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37. An orexigenic subnetwork within the human hippocampus
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Barbosa, Daniel A. N., Gattas, Sandra, Salgado, Juliana S., Kuijper, Fiene Marie, Wang, Allan R., Huang, Yuhao, Kakusa, Bina, Leuze, Christoph, Luczak, Artur, Rapp, Paul, Malenka, Robert C., Hermes, Dora, Miller, Kai J., Heifets, Boris D., Bohon, Cara, McNab, Jennifer A., and Halpern, Casey H.
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- 2023
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38. Neurons learn by predicting future activity
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Luczak, Artur, McNaughton, Bruce L, and Kubo, Yoshimasa
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Basic Behavioral and Social Science ,Neurosciences ,Behavioral and Social Science ,Mental Health ,Underpinning research ,1.1 Normal biological development and functioning ,Mental health ,Neurological - Abstract
Understanding how the brain learns may lead to machines with human-like intellectual capacities. It was previously proposed that the brain may operate on the principle of predictive coding. However, it is still not well understood how a predictive system could be implemented in the brain. Here we demonstrate that the ability of a single neuron to predict its future activity may provide an effective learning mechanism. Interestingly, this predictive learning rule can be derived from a metabolic principle, where neurons need to minimize their own synaptic activity (cost), while maximizing their impact on local blood supply by recruiting other neurons. We show how this mathematically derived learning rule can provide a theoretical connection between diverse types of brain-inspired algorithms, thus, offering a step toward development of a general theory of neuronal learning. We tested this predictive learning rule in neural network simulations and in data recorded from awake animals. Our results also suggest that spontaneous brain activity provides "training data" for neurons to learn to predict cortical dynamics. Thus, the ability of a single neuron to minimize surprise: i.e. the difference between actual and expected activity, could be an important missing element to understand computation in the brain.
- Published
- 2022
39. Estimating Likelihood of Dementia in the Absence of Diagnostic Data: A Latent Dementia Index in 10 Genetically Informed Studies
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Beam, Christopher R, Luczak, Susan E, Panizzon, Matthew S, Reynolds, Chandra A, Christensen, Kaare, Aslan, Anna K Dahl, Elman, Jeremy A, Franz, Carol E, Kremen, William S, Lee, Teresa, Nygaard, Marianne, Sachdev, Perminder S, Whitfield, Keith E, Pedersen, Nancy L, Gatz, Margaret, and Consortium, for the IGEMS
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Biological Psychology ,Psychology ,Dementia ,Alzheimer's Disease including Alzheimer's Disease Related Dementias (AD/ADRD) ,Brain Disorders ,Neurodegenerative ,Clinical Research ,Aging ,Acquired Cognitive Impairment ,Alzheimer's Disease ,Neurological ,Humans ,Activities of Daily Living ,Probability ,genetic correlation ,harmonization ,latent index ,twin study ,IGEMS Consortium ,quality of life ,Clinical Sciences ,Neurosciences ,Cognitive Sciences ,Neurology & Neurosurgery ,Clinical sciences ,Biological psychology - Abstract
BackgroundEpidemiological research on dementia is hampered by differences across studies in how dementia is classified, especially where clinical diagnoses of dementia may not be available.ObjectiveWe apply structural equation modeling to estimate dementia likelihood across heterogeneous samples within a multi-study consortium and use the twin design of the sample to validate the results.MethodsUsing 10 twin studies, we implement a latent variable approach that aligns different tests available in each study to assess cognitive, memory, and functional ability. The model separates general cognitive ability from components indicative of dementia. We examine the validity of this continuous latent dementia index (LDI). We then identify cut-off points along the LDI distributions in each study and align them across studies to distinguish individuals with and without probable dementia. Finally, we validate the LDI by determining its heritability and estimating genetic and environmental correlations between the LDI and clinically diagnosed dementia where available.ResultsResults indicate that coordinated estimation of LDI across 10 studies has validity against clinically diagnosed dementia. The LDI can be fit to heterogeneous sets of memory, other cognitive, and functional ability variables to extract a score reflective of likelihood of dementia that can be interpreted similarly across studies despite diverse study designs and sampling characteristics. Finally, the same genetic sources of variance strongly contribute to both the LDI and clinical diagnosis.ConclusionThis latent dementia indicator approach may serve as a model for other research consortia confronted with similar data integration challenges.
- Published
- 2022
40. A note on the Markovian SIR epidemic on a random graph with given degrees
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Luczak, Malwina
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Mathematics - Probability ,05C80, 60F99, 60J28, 92D30 - Abstract
This paper provides an additional probabilistic interpretation of the limiting functions for the SIR epidemic on the configuration model derived in the paper by Janson, Luczak and Windridge (2014)., Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1308.5493
- Published
- 2021
41. Final results of the LOPES radio interferometer for cosmic-ray air showers
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Apel, W. D., Arteaga-Velázquez, J. C., Bähren, L., Bekk, K., Bertaina, M., Biermann, P. L., Blümer, J., Bozdog, H., Cantoni, E., Chiavassa, A., Daumiller, K., de Souza, V., Di Pierro, F., Doll, P., Engel, R., Falcke, H., Fuchs, B., Gemmeke, H., Grupen, C., Haungs, A., Heck, D., Hörandel, J. R., Horneffer, A., Huber, D., Huege, T., Isar, P. G., Kampert, K. -H., Kang, D., Krömer, O., Kuijpers, J., Link, K., Luczak, P., Ludwig, M., Mathes, H. J., Melissas, M., Morello, C., Nehls, S., Oehlschläger, J., Palmieri, N., Pierog, T., Rautenberg, J., Rebel, H., Roth, M., Rühle, C., Saftoiu, A., Schieler, H., Schmidt, A., Schoo, S., Schröder, F. G., Sima, O., Toma, G., Trinchero, G. C., Weindl, A., Wochele, J., Zabierowski, J., Zensus, J. A., and Collaboration, LOPES
- Subjects
Astrophysics - High Energy Astrophysical Phenomena ,Astrophysics - Instrumentation and Methods for Astrophysics - Abstract
LOPES, the LOFAR prototype station, was an antenna array for cosmic-ray air showers operating from 2003 - 2013 within the KASCADE-Grande experiment. Meanwhile, the analysis is finished and the data of air-shower events measured by LOPES are available with open access in the KASCADE Cosmic Ray Data Center (KCDC). This article intends to provide a summary of the achievements, results, and lessons learned from LOPES. By digital, interferometric beamforming the detection of air showers became possible in the radio-loud environment of the Karlsruhe Institute of Technology (KIT). As a prototype experiment, LOPES tested several antenna types, array configurations and calibration techniques, and pioneered analysis methods for the reconstruction of the most important shower parameters, i.e., the arrival direction, the energy, and mass-dependent observables such as the position of the shower maximum. In addition to a review and update of previously published results, we also present new results based on end-to-end simulations including all known instrumental properties. For this, we applied the detector response to radio signals simulated with the CoREAS extension of CORSIKA, and analyzed them in the same way as measured data. Thus, we were able to study the detector performance more accurately than before, including some previously inaccessible features such as the impact of noise on the interferometric cross-correlation beam. These results led to several improvements, which are documented in this paper and can provide useful input for the design of future cosmic-ray experiments based on the digital radio-detection technique., Comment: Accepted for publication by EPJ C
- Published
- 2021
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42. The effect of foot posture on static balance, ankle and knee proprioception in 18-to-25-year-old female student: a cross-sectional study
- Author
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Maryam Ghorbani, Rasoul Yaali, Hassan Sadeghi, and Tony Luczak
- Subjects
Balance control ,Position sense ,Flexible pes planus ,Ankle and knee joints ,Diseases of the musculoskeletal system ,RC925-935 - Abstract
Abstract Background & purpose Afferent input from the sole affects postural stability. Cutaneous reflexes from the foot are important to posture and gait. Lower-limb afferents alone provide enough information to maintain upright stance and are critical in perceiving postural sway. Altered feedback from propreoceptive receptors alters gait and patterns of muscle activation. The position and posture of the foot and ankle may also play an important role in proprioceptive input.Therefore, the current research aims to compare static balance and ankle and knee proprioception in people with and without flexible flatfeet. Methodology 91 female students between the ages of 18 and 25 voluntarily participated in this study, of which 24 were in the flexible flatfoot group and 67 were in the regular foot group after evaluating the longitudinal arch of the foot. The position sense of ankle and knee joints were measured using the active reconstruction test of the ankle and knee angle; Static balance was measured using the Sharpened Romberg test. Data were non-normally distributed. Accordingly, non-parametric tests were applied. The Kruskal-Wallis test was applied to compare differences between groups in variables. Result Kruskal-Wallis test showed a significant difference between two groups of flat feet and normal feet in the variables of static balance and position sense of ankle plantarflexion, ankle dorsiflexion, and knee flexion (p ≤ 0.05). A significant correlation was found between static balance and sense of ankle and knee position in the group with normal feet. The analysis of the regression line also showed that ankle and knee position sense could predict the static balance score in the regular foot group (ankle dorsiflexion position sense 17% (R2 = 0.17), ankle plantarflexion position sense 17% (R2 = 0.17) and knee flexion position sense 46% (R2 = 0.46) explain of changes in static balance). Discussion & conclusion Flexible flatfoot soles can cause loss of balance and sense of joint position; therefore, according to this preliminary study, clinicians must be aware and should take into account this possible deficit in the management of these patients.
- Published
- 2023
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43. Correction: Data-driven analyses of motor impairments in animal models of neurological disorders.
- Author
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Hardeep Ryait, Edgar Bermudez-Contreras, Matthew Harvey, Jamshid Faraji, Behroo Mirza Agha, Andrea Gomez-Palacio Schjetnan, Aaron Gruber, Jon Doan, Majid Mohajerani, Gerlinde A S Metz, Ian Q Whishaw, and Artur Luczak
- Subjects
Biology (General) ,QH301-705.5 - Abstract
[This corrects the article DOI: 10.1371/journal.pbio.3000516.].
- Published
- 2024
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44. Comprehensive proteomics of monocytes indicates oxidative imbalance functionally related to inflammatory response in chronic kidney disease-related atherosclerosis
- Author
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Joanna Watral, Dorota Formanowicz, Bartłomiej Perek, Katarzyna Kostka-Jeziorny, Alina Podkowińska, Andrzej Tykarski, and Magdalena Luczak
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chronic kidney disease ,cardiovascular disease ,oxidative stress ,inflammation ,monocytes ,proteomics ,Biology (General) ,QH301-705.5 - Abstract
Atherosclerosis-induced cardiovascular events are the leading cause of mortality in chronic kidney disease (CKD) patients. Monocytes are involved in the formation of atherosclerotic plaques and mediate in the overproduction of ROS, promoting inflammation and oxidative stress. However, the relationship between monocytes, inflammation, and oxidative status in CKD-associated atherosclerosis has not been thoroughly investigated. Monocytes and plasma derived from two groups of CKD patients with varying degrees of atherosclerosis and two groups of patients with cardiovascular disease (CVD) and non-CKD atherosclerosis were analyzed. This study was designed to perform a comprehensive proteomic analysis of monocytes in combination with functional bioinformatics. In addition, a targeted investigation of oxidative stress- and inflammatory-related factors to explore CKD-associated atherosclerosis was applied. Dysregulation of proteins involved in lipid oxidation, cell survival, ROS synthesis and metabolism, and inflammatory responses has been revealed. The characteristic disturbances in the monocyte proteome changed with the progression of CKD. A closer examination of oxidative stress’s triggers, mediators, and effects on protein and lipid levels showed alterations in the oxidative imbalance between CKD and CVD. CKD monocytes demonstrated a significant increase of oxidized glutathione without changing the level of its reduced form. Evaluation of enzymatic antioxidants, sources of ROS, and modifications caused by ROS also revealed significant alterations between the study groups. In CKD, inflammation and oxidative imbalance correlated and drove each other. However, in CVD, oxidative stress-related factors were associated with each other but not to inflammatory proteins. Moreover, lipid abnormalities were more specific to classical CVD and unrelated to CKD. Such a comprehensive characterization of monocytes and oxidative stress in CKD and CVD patients has never been presented so far. Obtained results support the involvement of distinct mechanisms underlying the acceleration of atherosclerotic and non-atherosclerotic CKD.
- Published
- 2024
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45. Do research collaborations age like wine? Absolute and relative measures of CANZUK research partnerships’ strength since the 1950s
- Author
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Ba Xuan Nguyen, Markus Luczak-Roesch, and Jesse David Dinneen
- Subjects
Medicine ,Science - Published
- 2024
46. The Ramsey number of a long even cycle versus a star
- Author
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Allen, Peter, Łuczak, Tomasz, Polcyn, Joanna, and Zhang, Yanbo
- Subjects
Mathematics - Combinatorics ,05C55 (Primary), 05C35, 05C38 (Secondary) - Abstract
We find the exact value of the Ramsey number $R(C_{2\ell},K_{1,n})$, when $\ell$ and $n=O(\ell^{10/9})$ are large. Our result is closely related to the behaviour of Tur\'an number $ex(N, C_{2\ell})$ for an even cycle whose length grows quickly with $N$.
- Published
- 2020
47. $M$-estimation and deconvolution in a diffusion model with application to biosensor transdermal blood alcohol monitoring
- Author
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Allayioti, Maria, Bartroff, Jay, Liu, Haoxing, Goldstein, Larry, Luczak, Susan, and Rosen, Gary
- Subjects
Statistics - Applications ,Statistics - Methodology ,62F10 (Primary) 62F12, 62P10 (Secondary) - Abstract
We develop $M$-estimation and deconvolution methodology with the goal of making well-founded statistical inference on an individual's blood alcohol level based on noisy measurements of their skin alcohol content. We first apply our results to a nonlinear least squares estimator of the key parameter that specifies the blood/skin alcohol relation in a diffusion model, and establish its existence, consistency, and asymptotic normality. To make inference on the unknown underlying blood alchohol curve, we develop a basis space deconvolution approach with regulazation, and determine the asymptotic distribution of the error process, thus allowing us to compute uniform confidence bands on the curve. Simulation studies show agreement between the performance of our curve estimators and their asymptotic distributions at low noise levels, and we apply our methods to a real skin alcohol data set collected via a transdermal biosensor., Comment: 46 pages, 13 figures. This version adds a deconvolution method using a basis space approach with regularization in order to make inference on the true underlying blood alcohol curve, a subsequent derivation of the asymptotic error process and evaluations of the resulting theoretical uniform confidence bands via simulations
- Published
- 2020
48. Andr\'asfai and Vega graphs in Ramsey-Tur\'an theory
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Łuczak, Tomasz, Polcyn, Joanna, and Reiher, Christian
- Subjects
Mathematics - Combinatorics ,05C35 - Abstract
Given positive integers $n\ge s$, we let ${\mathrm{ex}}(n,s)$ denote the maximum number of edges in a triangle-free graph $G$ on $n$ vertices with $\alpha(G)\le s$. In the early sixties Andr\'{a}sfai conjectured that for $n/3
- Published
- 2020
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49. On the Ramsey-Tur\'an density of triangles
- Author
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Łuczak, Tomasz, Polcyn, Joanna, and Reiher, Christian
- Subjects
Mathematics - Combinatorics ,05C35, 05C69 - Abstract
One of the oldest results in modern graph theory, due to Mantel, asserts that every triangle-free graphs on $n$ vertices has at most $\lfloor n^2/4\rfloor$ edges. About half a century later Andr\'asfai studied dense triangle-free graphs and proved that the largest triangle-free graphs on $n$ vertices without independent sets of size $\alpha n$, where $2/5\le \alpha < 1/2$, are blow-ups of the pentagon. More than 50 further years have elapsed since Andr\'asfai's work. In this article we make the next step towards understanding the structure of dense triangle-free graphs without large independent sets. Notably, we determine the maximum size of triangle-free graphs~$G$ on $n$ vertices with $\alpha (G)\ge 3n/8$ and state a conjecture on the structure of the densest triangle-free graphs $G$ with $\alpha(G) > n/3$. We remark that the case $\alpha(G) \le n/3$ behaves differently, but due to the work of Brandt this situation is fairly well understood., Comment: Revised according to referee reports
- Published
- 2020
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50. Long monochromatic even cycles in 3-edge-coloured graphs of large minimum degree
- Author
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Łuczak, Tomasz and Rahimi, Zahra
- Subjects
Mathematics - Combinatorics ,05C55 (Primary), 05C38 (Secondary) - Abstract
We show that for every $\eta>0$, there exists $n_0$ such that for every even $n$, $n\ge n_0$, and every graph $G$ with $(2+\eta)n$ vertices and minimum degree at least $(7/4+4\eta)n$, each colouring of the edges of $G$ with three colours results in a monochromatic cycle of length $n$.
- Published
- 2020
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