Miracle-dz/UniFAR-FTUs huggingface dataset:
Fast, Accurate Frequency Estimators

The problem of estimating the frequency of a tone contaminated with noise appears in communications, audio, medical, instrumentation, and other applications. The fundamental tool for resolving this problem is the discrete Fourier transform (DFT) or its efficient cousin, the fast Fourier transform (FFT). When using either of them, a well-known tradeoff exists between the amount of time needed to collect data, the number of data points collected, the type of time-domain window used, and the resolution that can be achieved in the frequency domain. This article presents computationally simple algorithms that provide substantial refinement of the frequency estimation of tones based on DFT samples without the need for increasing the DFT size.
BROWN REPRESENTABILITY FOR STABLE CATEGORIES

This paper proves Brown Representability for stable categories. These categories are obtained from additive categories by declaring all morphisms which factor through objects from a fixed pre-enveloping class to be zero. Brown Representability for such categories is obtained by first proving that stable categories are what Brown in [2] calls ‘‘abstract homotopy categories’’, next using Brown’s theory for these categories. The result is applied to two cases: one is a category of complexes of modules over a ring. Here we recover a representability theorem for functors on derived categories, first given by Neeman in [11, Thm. 3.1]. The other case is the category of modules over an Artinian ring. Here we obtain a result on representability, Theorem 4.4, which appears to be new.
Induced polarization effects in inductive source electromagnetic data

Induced polarization (IP) surveys are commonly conducted to map the distribution of electrical chargeability, a diagnostic physical property in mineral exploration and in many environmental problems. Although these surveys have been successful in the past, the galvanic sources required make their application labour intensive and prevents them from being applied in some geological settings. The ability to detect chargeability with a geophysical technique that employs inductive sources, eliminating the need to inject current directly into the ground, would provide a valuable tool to applied geophysicists. In this work, two aspects of inductive source induced polarization are examined. First, a new methodology for processing inductive source frequency domain EM data to identify IP effects is presented. The method makes use of the asymptotic behaviour of the secondary magnetic fields at low frequency. A new quantity, referred to as the ISIP datum, is defined so that it equals zero at low frequencies for any frequency-independent (nonchargeable) conductivity distribution. Thus, any non-zero response in the ISIP data indicates the presence of chargeable material. Numerical simulations demonstrate that the method can be applied even in complicated geological situations. A 3D inversion algorithm is developed to recover the chargeability from the ISIP data and the inversion is demonstrated on synthetic examples. Understanding the impacts of IP effects on time-domain electromagnetic data requires the ability to simulate common survey techniques while taking chargeability into account. Most existing techniques preform this modelling in the frequency domain prior to transforming their results to the time domain. Application of those techniques on three dimensional problems can
Comment on “Reference priors for high energy physics”

A Bayesian reference analysis of a typical scenario of high energy physics has recently been performed [Phys. Rev. D 82, 034002 (2010)]. The reference prior with partial information (and hence also the posterior) were found to depend on the sequence of subsets of the parameter space used for a normalization process. A particular choice of the subsets leading to a proper posterior was advocated. Here it is shown that this choice differs from the natural sequence of subsets in the ``original parametrization'' of the problem, which has been generally recommended elsewhere. Although this questions the manner in which the commented result was obtained, the result itself is corroborated because the present derivation based on a different argument yields a reference prior of the same functional form.
Tarski on models and logical consequence

An essential notion in semantics is that of logical consequence. A sentence P is a logical consequence of a set of sentences S if and only if it is not possible for the sentences in S to be true and the sentence P to be false at the same time. This is basically the definition (although given in the more abstract terminology of models) that Tarski gave of logical consequence in 1936. In the last twenty years there has been a heated debate on the exact nature of Tarski's theory of logical consequence. This debate has important consequences for the philosophical problem of giving an exact characterization of this central notion in philosophy. Moreover, the intense focus on the original publication by Tarski has led to several disagreements with respect to important interpretative issues related to Tarski's contribution. This chapter provides evidence to show that in 1936 (and 1940) Tarski defended a notion of logical consequence (based on a fixed domain conception) that is at odds with the model-theoretic one common today. The addendum to the chapter defends the interpretation against recent criticism by Gomez-Torrente.
Elevated blood pressure accelerates white matter brain aging among late middle-aged women: a Mendelian Randomization study in the UK Biobank

Background: Elevated blood pressure (BP) is a modifiable risk factor associated with cognitive impairment and cerebrovascular diseases. However, the causal effect of BP on white matter brain aging remains unclear. Methods: In this study, we focused on N = 228 473 individuals of European ancestry who had genotype data and clinical BP measurements available (103 929 men and 124 544 women, mean age = 56.49, including 16 901 participants with neuroimaging data available) collected from UK Biobank (UKB). We first established a machine learning model to compute the outcome variable brain age gap (BAG) based on white matter microstructure integrity measured by fractional anisotropy derived from diffusion tensor imaging data. We then performed a two-sample Mendelian randomization analysis to estimate the causal effect of BP on white matter BAG in the whole population and subgroups stratified by sex and age brackets using two nonoverlapping data sets. Results: The hypertension group is on average 0.31 years (95% CI = 0.13–0.49; P < 0.0001) older in white matter brain age than the nonhypertension group. Women are on average 0.81 years (95% CI = 0.68–0.95; P < 0.0001) younger in white matter brain age than men. The Mendelian randomization analyses showed an overall significant positive causal effect of DBP on white matter BAG (0.37 years/10 mmHg, 95% CI 0.034–0.71, P = 0.0311). In stratified analysis, the causal effect was found most prominent among women aged 50–59 and aged 60–69. Conclusion: High BP can accelerate white matter brain aging among late middle-aged women, providing insights on planning effective control of BP for women in this age group.
Evaluation of changes in coagulation factors in fresh frozen plasma during storage at -18C for 5 weeks at Kisii Teaching and Referral Hospital.

Background: Fresh frozen plasma is a critical substitute therapy in management of bleeding. Increased risk of venous thrombosis has been described to be associated with high plasma levels of several coagulation factors. Methodology: This study was a time series analysis of fresh frozen plasma stored at -18C for five weeks. A sample of 180 ml plasma was obtained from the blood centrifuged at 4000rpm which was aliquoted into three parts each containing 60ml. The first aliquot was used to assess the changes in coagulation factors in FFP at baseline during the first week of sample collection, the second aliquot was used to assess the changes in coagulation factors in FFP storage at -18C temp after three weeks of storage, the third aliquot was used to assess the changes in coagulation factors in FFP storage at -18C temp after five weeks of storage. Coagulation factor analysis was performed using Erba Mannheim ECL 105 coagulation analyzer, India factor results recorded. Thawing for subsequent coagulation factor analysis and serial testing of stored cryoprecipitate and fresh frozen plasma was done using Stericox Plasma Thawing Bath at 37C, for 45 mins before before analyzing the samples. Standard storage conditions for the aliquots were monitored and maintained to ensure homogeneity. Results: The findings showed significant changes in the coagulation factors in FFP during storage at -18 for a period to five weeks with chi-square value of 216.000 and asymptomatic significance value (p-value) <0.0001* less than the standard alpha 0.05. Conclusion: There was a constant decrease of coagulation factors in fresh frozen plasma during storage at -18C for 5 weeks at Kisii Teaching and Referral Hospital, Kisii County.
On the traces of certain classes of permuting mappings in rings

Abstract Let R be a semiprime ring with center Z and extended centroid C. For a fixed integer n ≥ 2, the trace δ:R→R${\delta \colon R\rightarrow R}$ of a permuting n-additive mapping D:R n →R${D\colon R^n\rightarrow R}$ is defined as δ(x)=D(x,.,x)${\delta (x)=D(x,\ldots ,x)}$ for all x ∈ R. The notion of permuting n-derivation was introduced by Park [J. Chungcheong Math. Soc. 22 (2009), no.3, 451–458] as follows: a permuting n-additive mapping Δ:R n →R${\Delta \colon R^n\rightarrow R}$ is said to be permuting n-derivation if Δ(x 1 ,x 2 ,⋯,x i x i ' ,⋯,x n )=Δ(x 1 ,x 2 ,⋯,x i ,⋯,x n )x i ' +x i Δ(x 1 ,x 2 ,⋯,x i ' ,⋯,x n )forallx i ,x i ' ∈R. $ \Delta (x_1,x_2,\dots , x_ix_i^{\prime },\dots , x_n)=\Delta (x_1,x_2,\dots , x_i,\dots , x_n)x_i^{\prime }+ x_i\Delta (x_1,x_2,\dots , x_i^{\prime },\dots , x_n)\quad \text{for all }x_i ,x_i^{\prime } \in R. $ A permuting n-additive mapping Ω:R n →R${\Omega \colon R^n\rightarrow R}$ is known to be a permuting generalized n-derivation if there exists a permuting n-derivation Δ:R n →R${\Delta \colon R^n\rightarrow R}$ such that Ω(x 1 ,x 2 ,⋯,x i x i ' ,⋯,x n )=Ω(x 1 ,x 2 ,⋯,x i ,⋯,x n )x i ' +x i Δ(x 1 ,x 2 ,⋯,x i ' ,⋯,x n )forallx i ,x i ' ∈R. $ \Omega (x_1,x_2,\dots , x_ix_i^{\prime },\dots , x_n)=\Omega (x_1,x_2,\dots , x_i,\dots , x_n)x_i^{\prime }+ x_i\Delta (x_1,x_2,\dots , x_i^{\prime },\dots , x_n)\quad \text{for all }x_i ,x_i^{\prime } \in R. $ The main result of this paper states that if I is a nonzero ideal of a semiprime ring R and Δ:R n →R${\Delta :R^n\rightarrow R}$ is a permuting n-derivation such that Δ(I,.,I)≠{0}${\Delta (I,\ldots ,I)\ne \lbrace 0\rbrace }$ and [δ(x),x]=0${[\delta (x),x]=0}$ for all x ∈ I, where δ is the trace of Δ, then R contains a nonzero central ideal. Furthermore, some related results are also proven.
Diffusion models with location-scale noise

Diffusion Models (DMs) are powerful generative models that add Gaussian noise to the data and learn to remove it. We wanted to determine which noise distribution (Gaussian or non-Gaussian) led to better generated data in DMs. Since DMs do not work by design with non-Gaussian noise, we built a framework that allows reversing a diffusion process with non-Gaussian location-scale noise. We use that framework to show that the Gaussian distribution performs the best over a wide range of other distributions (Laplace, Uniform, t, Generalized-Gaussian).
Scale-Equivariant Deep Learning for 3D Data

The ability of convolutional neural networks (CNNs) to recognize objects regardless of their position in the image is due to the translation-equivariance of the convolutional operation. Group-equivariant CNNs transfer this equivariance to other transformations of the input. Dealing appropriately with objects and object parts of different scale is challenging, and scale can vary for multiple reasons such as the underlying object size or the resolution of the imaging modality. In this paper, we propose a scale-equivariant convolutional network layer for three-dimensional data that guarantees scale-equivariance in 3D CNNs. Scale-equivariance lifts the burden of having to learn each possible scale separately, allowing the neural network to focus on higher-level learning goals, which leads to better results and better data-efficiency. We provide an overview of the theoretical foundations and scientific work on scale-equivariant neural networks in the two-dimensional domain. We then transfer the concepts from 2D to the three-dimensional space and create a scale-equivariant convolutional layer for 3D data. Using the proposed scale-equivariant layer, we create a scale-equivariant U-Net for medical image segmentation and compare it with a non-scale-equivariant baseline method. Our experiments demonstrate the effectiveness of the proposed method in achieving scale-equivariance for 3D medical image analysis. We publish our code at https://github.com/wimmerth/scale-equivariant-3d-convnet for further research and application.
Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications

The occurrence of singularities where spacetime curvature becomes infinite and geodesic evolution breaks down are inevitable events in classical general relativity (GR) unless one chooses an exotic matter violating weak energy condition. These singularities show up in various physical processes, such as the gravitational collapse, the birth of the universe in the standard cosmology as well as the classical solutions of the black hole spacetimes. In the last two decades, a rigorous understanding of the dynamics of quantum spacetime and the way it resolves singularities has been achieved in loop quantum cosmology (LQC) which applies the concepts and techniques of loop quantum gravity to the symmetry reduced cosmological spacetimes. Due to the fundamental discreteness of quantum geometry derived from the quantum theory, the big bang singularity has been robustly shown to be replaced by a big bounce. Strong curvature singularities intrinsic in the classical cosmology are generically resolved for a variety of cosmological spacetimes including anisotropic models and polarized Gowdy models. Using effective spacetime description the LQC universe also provides an ultra-violet complete description of the classical inflationary scenario as well as its alternatives such as the ekpyrotic and matter bounce scenarios. In this chapter we provide a summary of singularity resolution and its physical implications for various isotropic and anisotropic cosmological spacetimes in LQC and analyze robustness of results through variant models originating from different quantization prescriptions.
Prospective Elementary Teachers' Conceptions of Unitizing with Whole Numbers and Fractions.

This article examines prospective elementary teachers’ conceptions of unitizing with whole numbers and fraction concepts and operations throughout a semester-long mathematics content course. Student work samples and classroom conversations are used to illustrate the types of unitizing understandings that prospective teachers bring to teacher education programs. The results indicate that the prospective teachers were successful with iterating units and developing composite units within both whole numbers and fractions. Although this did not indicate they had a complete understanding of unitizing, the results imply that tools, such as number lines, may be useful in determining what understandings they do have.
Thermal quenching of classical and semiclassical chaos

The growth rate of out-of-time ordered correlators (OTOCs) provide for the notion of a quantum Lyapunov exponent, which quantiﬁes chaos and information scrambling in quantum systems. In thermal ensembles, this growth rate is reduced from its corresponding value in the microcanonical distribution, and a temperature-dependent bound on has been conjectured to exist for the quantum Lyapunov exponent. We detail a two-fold mechanism which is responsible for the reduction of the Lyapunov exponents in thermal quantum systems
Bit-Interleaved Multiple Access: Improved Fairness, Reliability, and Latency for Massive IoT Networks

Internet of Things (IoT) networks require massive connections in dense areas. Therefore, a resource-efficient multiple access scheme seems inevitable to enable immense connectivity where multiple devices have to share the same resource block (RB). Nonorthogonal multiple access (NOMA) has been considered as the strongest candidate in recent years. However, in this article, by considering the practical implementation, we first provide a true power allocation (PA) constraint with finite alphabet inputs for conventional downlink NOMA and demonstrate that it cannot support massive connections in practical systems. To this end, we propose the bit-interleaved multiple access (BIMA) scheme in downlink IoT networks. The proposed BIMA scheme implements bitwise multiaccess interleaving and deinterleaving at the transceiver ends and there are no strict PA constraints, unlike conventional NOMA, thus allowing a high number of devices in the same RB. We provide a comprehensive analytical framework for BIMA by investigating all key performance indicators (KPIs) to present both information-theoretic [i.e., ergodic capacity (EC) and outage probability (OP)] and finite alphabet inputs [i.e., bit error rate (BER)] performance metrics with both instantaneous and statistical channel ordering. In addition, we define Jain’s fairness index and proportional fairness index (PFI) in terms of all KPIs. Based on the extensive computer simulations, we reveal that BIMA outperforms conventional NOMA significantly, with a performance gain of up to 20–30 dB in terms of KPIs in some scenarios. In other words, compared to conventional NOMA schemes, the same KPIs are met in BIMA with 20–30 dB less transmit power, which is quite promising for energy-limited use cases. Moreover, this performance gain becomes greater when more IoT devices are supported. BIMA provides a full diversity order for all IoT devices and enables the implementation of an arbitrary number of devices and modulation orders, which is crucial for IoT networks where a huge number of devices should be supported in a single RB in dense areas. In addition to the overall performance gain, BIMA guarantees a fairness system where none of the devices gets a severely degraded performance and the sum-rate is shared in a fair manner among devices. It guarantees QoS satisfaction for all devices. Finally, we provide an intense complexity and latency analysis for BIMA and demonstrate that it provides lower latency compared to conventional NOMA receivers, since it allows parallel computation at the receivers and no iterative operations are required. We show that compared to conventional NOMA receivers, BIMA reduces latency by up to 350% for specific IoT devices and 170% on average.
Asymmetry and tighter uncertainty relations for Rényi entropies via quantum-classical decompositions of resource measures

It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is discussed, with the quantum contribution specified by a measure of the noncommutativity of a given set of operators relative to the quantum state, and the classical contribution generated by the mixedness of the state. Suitable measures of noncommutativity or 'quantumness' include quantum Fisher information, and the asymmetry of a given set, group or algebra of operators, and are generalised to nonprojective observables and quantum channels. Strong entropic uncertainty relations and lower bounds for R\'enyi entropies are obtained, valid for arbitrary discrete observables, that take the mixedness of the state into account via a classical contribution to the lower bound. These relations can also be interpreted without reference to quantum-classical decompositions, as tradeoff relations that bound the asymmetry of one observable in terms of the entropy of another.
Statistical state dynamics-based study of the stability of the mean statistical state of wall-bounded turbulence

Turbulence in wall-bounded flows is characterized by stable statistics. Although, in many turbulent systems, this stable statistical state corresponds to a stable fixed point of an associated statistical state dynamics (SSD) closed at second order, referred to as S3T, this is not the case for wall turbulence. In wall-turbulence the trajectory of the statistical state is on a transient chaotic attractor in the S3T statistical state space and the time-mean statistical state is neither a stable fixed point of this SSD nor, if it is maintained as an equilibrium, is it stable. Nevertheless, sufficiently small perturbations from the ensemble/time-mean state relax back to the mean statistical state following an effective linear dynamics. In this work, the dynamics of spanwise uniform perturbations to the time-mean flow are studied using a linear inverse model (LIM) to identify the linear operator governing the ensemble stability of the ensemble/time-mean state by obtaining the time-mean stability properties over the transient attractor of the turbulence identified by the S3T SSD. The ensemble/time-mean stability of an unstable equilibrium can be understood by noting that even when every member of an ensemble is unstable the ensemble mean may be stable with perturbations following stable dynamics. While simplifying insight into turbulent flows has been obtained by identifying and studying ensemble mean statistical states, less attention has been accorded to identifying and studying the ensemble mean dynamics. We show that in the case of wall turbulence, even though stable fixed point SSD equilibria are not available to allow the application of traditional perturbation analysis methods to identify the perturbation stability of the mean state, an effective linear stability analysis can be obtained to identify the perturbation dynamics of the ensemble/time-mean statistical state.
Learning coordination through new actions

We provide a novel approach to achieving a desired outcome in a coordination game: the original 2x2 game is embedded in a 2x3 game where one of the players may use a third action. For a large set of payoff values only one of the Nash equilibria of the original 2x2 game is stable under replicator dynamics. We show that this Nash equilibrium is the {\omega}-limit of all initial conditions in the interior of the state space for the modified 2x3 game. Thus, the existence of a third action for one of the players, although not used, allows both players to coordinate on one Nash equilibrium. This Nash equilibrium is the one preferred by, at least, the player with access to the new action. This approach deals with both coordination failure (players choose the payoff-dominant Nash equilibrium, if such a Nash equilibrium exists) and miscoordination (players do not use mixed strategies).
Feasibility, Opportunities, and Challenges of Utilizing AI for Collaborative Qualitative Analysis

While individual-level AI-assisted analysis has been fairly examined in prior work, AI-assisted collaborative qualitative analysis (CQA) remains an under-explored area of research. After identifying CQA behaviors and design opportunities through interviews, we propose our collaborative qualitative coding tool, CoAIcoder , and present the results of our studies that examine how AI-assisted CQA can work. We then designed a between-subject design with 32 pairs of novice users to perform CQA across three commonly practiced phases under four collaboration methods. Our results show that CoAIcoder (with AI & Shared Model) could potentially improve the coding efficiency of CQA, however, with a potential risk of decreasing the code diversity. We also highlight the relationship between independence level and coding outcome, as well as the trade-off between, on the one hand, Coding Time & IRR, and on the other hand Code Diversity. We lastly identified design implications to inspire the future design of CQA systems.