Miracle-dz/UniFAR-FTUs huggingface dataset:
Trans-Planckian Issue in the Milne Universe

The ``trans-Planckian'' challenge in cosmology appears when we trace the present physical wavelengths of fluctuations backwards in time. They become smaller and smaller until crossing the Planck scale where conventional QFT is challenged, so that unknown ultraviolet physics may be traced in the observable cosmological fluctuations. Usually this issue is addressed in the inflationary context, but trans-Planckian reasoning is much broader. We examine this logic in a simple example of scalar quantum field theory in the expanding and contracting Milne universes, where wavelengths of the eigenmodes are red- or blue-shifted. Trans-Planckian modifications of QFT should result in a UV-dependent VeV of the energy momentum tensor of a scalar field in the Milne universe. On the other hand, the Milne universe is another coordinate systems of flat Minkowski space-time, and the covariant energy momentum tensor should be the same (but vacuum-dependent) in different coordinates of flat space time. We explicitly demonstrate that in conventional QFT the energy momentum tensor, choosing the adiabatic vacuum, is identical to zero in Minkowski coordinates, and remains zero in the contracting Milne universe (due to non-trivial cancellations of contributions from particles which appear in the accelerating frame and from vacuum polarization there). In contrast to this, the trans-Planckian modification of the energy momentum tensor is not motivated. We provide a similar argument for the expanding Milne universe, where the energy momentum tensor in the conformal vacuum is non-zero. Similar arguments are applicable for other cosmological models where the curvature is much lower than Planckian which leads to conflicts with trans-Planckian considerations.
Experimental electronic structure of In2O3 and Ga2O3

Transparent conducting oxides (TCOs) pose a number of serious challenges. In addition to the pursuit of high-quality single crystals and thin films, their application has to be preceded by a thorough understanding of their peculiar electronic structure. It is of fundamental interest to understand why these materials, transparent up to the UV spectral regime, behave also as conductors. Here we investigate In2O3 and Ga2O3, two binary oxides, which show the smallest and largest optical gaps among conventional n-type TCOs. The investigations on the electronic structure were performed on high-quality n-type single crystals showing carrier densities of ∼1019 cm−3 (In2O3) and ∼1017 cm−3 (Ga2O3). The subjects addressed for both materials are: the determination of the band structure along high-symmetry directions and fundamental gaps by angular resolved photoemission (ARPES). We also address the orbital character of the valence- and conduction-band regions by exploiting photoemission cross sections in x-ray photoemission (XPS) and by x-ray absorption (XAS). The observations are discussed with reference to calculations of the electronic structure and the experimental results on thin films.
An Approach to Linear Programming under Uncertainty

A solution is given to a programming problem under uncertainty when the distribution function of demand is discrete and the cost structure assumes a certain type. The resulting objective function is convex, but not necessarily separable. With a rather simple change in variables, the solution of the stochastic problem is shown to be equivalent to the solution of a linear program.
The existence of closed 3-forms of $\tilde G_2$-type on 7-manifolds

In this note we construct a first example of a closed 3-form of $\tilde G_2$-type on $S^3\times S^4$. We prove that $S^3\times S^4$ does not admit a homogeneous 3-form of $\tilde G_2$-type. Thus our example is a first example of a closed 3-form of $\tilde G_2$-type on a compact 7-manifold which is not stably homogeneous.
CLT for Ornstein-Uhlenbeck branching particle system

In this paper we consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in $\Rd$ and undergoing a binary, supercritical branching with a constant rate $\lambda>0$. This system is known to fulfil a law of large numbers (under exponential scaling). In the paper we prove the corresponding central limit theorem. The limit and the CLT normalisation fall into three qualitatively different classes. In, what we call, the small branching rate case the situation resembles the classical one. The weak limit is Gaussian and normalisation is the square root of the size of the system. In the critical case the limit is still Gaussian, however the normalisation requires an additional term. Finally, when branching has large rate the situation is completely different. The limit is no longer Gaussian, the normalisation is substantially larger than the classical one and the convergence holds in probability. We prove also that the spatial fluctuations are asymptotically independent of the fluctuations of the total number of particles (which is a Galton-Watson process).
A Saddle Point Numerical Method for Helmholtz Equations

In a previous work, the author and D.C. Dobson proposed a numerical method for solving the complex Helmholtz equation based on the minimization variational principles developed by Milton, Seppecher, and Bouchitte. This method results in a system of equations with a symmetric positive definite coefficient matrix, but at the same time requires solving simultaneously for the solution and its gradient. Herein is presented a method based on the saddle point variational principles of Milton, Seppecher, and Bouchitte, which produces symmetric positive definite systems of equations, but eliminates the necessity of solving for the gradient of the solution. The result is a method for a wide class of Helmholtz problems based completely on the Conjugate Gradient algorithm.
Dynamic integration of depth maps

This paper deals with a data fusion technique for depth reconstruction which integrates regularization by variational methods with stochastic optimization based on Kalman filtering. A framework for the fusion of multiple regularized depth maps is proposed for on-line integration of many views of the visible scene. This kind of approach has some advantages in respect with similar ones, as it is stressed widely in the paper. It does not use optical flow, camera modeling or an explicit motion equation and can be used to fuse stochastically both sparse or dense depth data, obtaining reliable estimates in the whole image domain.
Equivalence of Riesz and Baez-Duarte criterion for the Riemann Hypothesis

W e investigate the relation between the Riesz and the Baez-D uarte criterion fortheRiem ann H ypothesis.In particularwepresenttherelation between the function R ( x )appearing in the Riesz criterion and the sequence c k appearing in the Baez-D uarte form ulation. It is shown that R ( x )can expressed by c k and viceversa thesequence c k can beobtained from the values of R ( x ) atinteger argum ents. W e give also som e relations involving c k and R ( x ),in particular value ofthe alternating sum of c k .
A deviation bound for $\alpha$-dependent sequences with applications to intermittent maps

We prove a deviation bound for the maximum of partial sums of functions of $\alpha$-dependent sequences as defined in Dedecker, Gou{\"e}zel and Merlev{\`e}de (2010). As a consequence, we extend the Rosenthal inequality of Rio (2000) for $\alpha$-mixing sequences in the sense of Rosenblatt (1956) to the larger class of $\alpha$-dependent sequences. Starting from the deviation inequality, we obtain upper bounds for large deviations and an H{\"o}lderian invariance principle for the Donsker line. We illustrate our results through the example of intermittent maps of the interval, which are not $\alpha$-mixing in the sense of Rosenblatt.
Von Neumann's inequality for tensors

For two matrices in $\mathbb R^{n_1\times n_2}$, the von Neumann inequality says that their scalar product is less than or equal to the scalar product of their singular spectrum. In this short note, we extend this result to real tensors and provide a complete study of the equality case.
Bialgebra coverings and transfer of
 structure

We introduce the bicategory of bialgebras with coverings (which can be thought of as coalgebra-indexed families of morphisms), and provide a motivating application to the transfer of formulas for primitives and antipode. Additionally, we study properties of this bicategory and various sub-bicategories, and describe some universal constructions. Finally, we generalize Nichols' result on bialgebra quotients of Hopf algebra, which gives conditions on when the resulting bialgebra quotient is a Hopf algebra.
On the quasisymmetric minimality of homogeneous perfect sets

Z. Wen and J. Wu introduced the notion of homogeneous perfect sets as a generalization of Cantor type sets and determined their exact Hausdorff dimension based on the length of their fundamental intervals and the gaps between them. In this paper, we considered the minimality of the homogeneous perfect sets with Hausdorff dimension 1 and proved they are 1-dimensional quasisymmetrically minimal under some conditions.
Sistemas dinámicos cardiacos en neonatos normales: Ley caótica cardiaca neonatal

Objective: To characterize mathematically normal cardiac dynamic on neonate in four states: Quiet asleep, Active asleep, Quiet awake, and Active awake, to develop a generalization determining all possible normal attractors. Materials and methods: Based on dynamic system theory, there were taken minimal and maximal RR intervals on a neonate in four behavioral states. Were made a simulation of cardiac dynamic frequency for each state building chaotic attractors. Later were quantified occupation spaces and fractal dimensions of the attractors on Box Counting general space, searching similarities and differences between these dynamic states. Finally there were calculated all possible normal attractors, based on an exponential law previously developed for adults cardiac dynamic. Results: There were found differences in every four behavioral states, comparing space occupation measures, which had values of 199 for S1, 131 for S2, 61 for S3 and 175 for S4 on Kp grille. Also there were found fractal dimension values distinguished for every state. Normal attractor's total number was 4602. Conclusion: There were developed a new a causal physical-mathematical methodology of neonate cardiac dynamic, which allow distinguish different behavioral states and establishment of all normal dynamics.
Structure change detection of images based on biological vision principle

Conventional methods to detect changes between temporal images are subject to the effect of illumination variance and registration noise. The method proposed in this paper uses the edge structure information in image to detect changes. A new conception based on biological vision principle, named Edge Token, is introduced to describe the edge structure, which is extracted by using a set of Gabor functions on the intensity map of gradient image. Correlation is used to compare the similarity of two Edge Token vectors. In order to reduce the false alarm, a suppression factor is taken to reduce the effect of weak edges. According to the result of the correlation process, decision rule can be made to locate the outline of changed area. The Edge Token based change detection is robust to illumination variance and registration noise. Experiments on simulated data and remote sensing images are presented.
Assessment of the Doi-Ohta theory for co-continuous blends under oscillatory flow

Predictions of the semiphenomenological Doi–Ohta theory for the rheology and morphology of immiscible blends are compared to experimental data of a 40/60 blend of PMMA/PαMSAN with a co-continuous structure. Since the Doi–Ohta theory actually was developed for co-continuous blends, published comparisons on droplet–matrix blends are not considered as adequate. It is verified how the polymeric constituents contribute to the blend response and it is shown how the phenomenological parameters of the Doi–Ohta theory can be determined. Subsequently, these parameters are used to predict the morphology evolution and rheological response of the blend under oscillatory flow. The evolution of the storage modulus clearly reflects the changes in morphology of the blend over time and strain amplitude in agreement with the theoretical predictions. Below a critical strain amplitude the co-continuous structure will coarsen until a droplet–matrix morphology is generated but large strain amplitudes are effective enough to sto.
Local asymptotic normality for randomly censored models with applications to rank tests

For randomly right censored models we study the asymptotic behaviour of linear (rank) statistics under local alternatives. The results can be used to evaluate the asymptotic power of the corresponding tests. For instance we treat the question how to choose the best scores in order to derive asymptotically optimal (rank) tests under certain alternatives.
Black hole mass formula in the membrane paradigm

The membrane paradigm approach adopts a timelike surface, stretched out off the null event horizon, to study several important black hole properties. We use this powerful tool to give a direct derivation of the black hole mass formula in the static and stationary cases without and with electric field. Since here the membrane is a self-gravitating material system we go beyond the usual applicability on test particles and test fields of the paradigm.
About the Cauchy problem in Stelle's quadratic gravity

The focus of the present work is on the Cauchy problem for the quadratic gravity models introduced in \cite{stelle,stelle2}. These are renormalizable higher order derivative models of gravity, but at cost of ghostly states propagating in the phase space. A previous work on the subject is [1]. The techniques employed here differ slightly from those in [2], but the main conclusions agree. Furthermore, the analysis of the initial value formulation in [3] is enlarged and the use of harmonic coordinates is clarified. In particular, it is shown that the initial constraints found [4] include a redundant one. In other words, this constraint is satisfied when the equations of motion are taken into account. In addition, some terms that are not specified in [5] are derived explicitly. This procedure facilitates application of some of the mathematical theorems given in [6]. As a consequence of these theorems, the existence of both C∞ solutions and maximal globally hyperbolic developments is proved. The obtained equations may be relevant for the stability analysis of the solutions under small perturbations of the initial data.
Near infrared spectroscopy based brain-computer interface

A brain-computer interface (BCI) provides users with an alternative output channel other than the normal output path of the brain. BCI is being given much attention recently as an alternate mode of communication and control for the disabled, such as patients suffering from Amyotrophic Lateral Sclerosis (ALS) or "locked-in". BCI may also find applications in military, education and entertainment. Most of the existing BCI systems which rely on the brain's electrical activity use scalp EEG signals. The scalp EEG is an inherently noisy and non-linear signal. The signal is detrimentally affected by various artifacts such as the EOG, EMG, ECG and so forth. EEG is cumbersome to use in practice, because of the need for applying conductive gel, and the need for the subject to be immobile. There is an urgent need for a more accessible interface that uses a more direct measure of cognitive function to control an output device. The optical response of Near Infrared Spectroscopy (NIRS) denoting brain activation can be used as an alternative to electrical signals, with the intention of developing a more practical and user-friendly BCI. In this paper, a new method of brain-computer interface (BCI) based on NIRS is proposed. Preliminary results of our experiments towards developing this system are reported.
GPGPU-Enabled Physics Based Deformed Model Simulation

Computer simulation techniques are widely adopted nowadays in many areas like manufacturing, engineering, graphics, animation, virtual reality and so on. However, the standard finite element based simulation is notorious for its expensive computation. To address this challenge, I present a GPU-based parallel implementation for simulating large elastic deformation. Classic modal analysis provides a set of orthonormal bases vectors, which span a spectral space encoding the dynamics of the elastic body. As each basis vector is orthogonal to each other, the computation is completely decoupled and can be well-fit into the modern GPGPU platform. We further explore the latest feature of NVIDIA CUDA so that the result of GPU computation can be directly used for upcoming rendering/visualization and a significant amount of overheads for transmitting data from client GPU and host CPU via the PCI-Express bus are avoided. Real-time simulation is made possible with this technique for many cases that otherwise is not possible.
Invertible K(2)–local E–modules in
C4–spectra

We compute the Picard group of the category of $K(2)$-local module spectra over the ring spectrum $E^{hC_4}$, where $E$ is a height 2 Morava $E$-theory and $C_4$ is a subgroup of the associated Morava stabilizer group. This group can be identified with the Picard group of $K(2)$-local $E$-modules in genuine $C_4$-spectra. We show that in addition to a cyclic subgroup of order 32 generated by $ E\wedge S^1$ the Picard group contains a subgroup of order 2 generated by $E\wedge S^{7+\sigma}$, where $\sigma$ is the sign representation of the group $C_4$. In the process, we completely compute the $RO(C_4)$-graded Mackey functor homotopy fixed point spectral sequence for the $C_4$-spectrum $E$.
The effect of operator variability and experience in vertebroplasty outcomes.

PURPOSE To determine if operator variability, prior vertebroplasty experience, or acquired vertebroplasty experience affects clinical outcomes. MATERIALS AND METHODS Informed consent was obtained from all patients and all data were handled in a manner consistent with institutional review board guidelines and the Health Insurance Portability and Accountability Act. Outcomes from 841 vertebroplasties, sorted by operator, were studied; two operators had previous vertebroplasty experience and five were neurointerventionalists who were initially new to the procedure. Objective (Roland-Morris Disability Questionnaire [RDQ] and analog pain scales) and subjective (mobility, narcotic use) scores were monitored before and after vertebroplasty at specified intervals following treatment. Perioperative cement volume utilization, complications, and number of treated levels were recorded. Random-effects and repeated-measures analyses of variance were used to assess operator differences and variability in clinical outcomes while generalized linear mixed-model regression analyses were used to track changes in clinical outcomes over time. RESULTS All operators provided similar average durable clinical improvements in postoperative pain and disability with nonsignificant interoperator variability. However, generalized linear model regression suggests that four of five initially novice operators showed significant changes in several procedural measures and clinical outcomes over the study timeframe, including cement volume utilization (reduction of 3.64 to 4.63 cm(3)), 1 week RDQ score (reduction of 4.79 to 8.62 points) and postoperative rest pain (reduction of 1.18 to 2.03 points). CONCLUSION Changes over time in measured outcomes suggest the presence of a training effect among novice operators. Cement volume utilization and immediate postprocedural pain decrease with experience but long-term clinical outcomes are insensitive to operator experience.
Characterization of polarization attributes of seismic waves using continuous wavelet transforms

Complex-trace analysis is the method of choice for analyzing polarized data. Because particle motion can be represented by instantaneous attributes that show distinct features for waves of different polarization characteristics, it can be used to separate and characterize these waves. Traditional methods of complex-trace analysis only give the instantaneous attributes as a function of time or frequency. However, for transient wave types or seismic events that overlap in time, an estimate of the polarization parameters requires analysis of the time-frequency dependence of these attributes. We propose a method to map instantaneous polarization attributes of seismic signals in the wavelet domain and explicitly relate these attributes with the wavelet-transform coefficients of the analyzed signal. We compare our method with traditional complex-trace analysis using numerical examples. An advantage of our method is its possibility of performing the complete wave-mode separation/filtering process in the wavelet .
The periodic table of topological insulators and superconductors: the loop sequence approach

In this work, a complete homotopic interpretation on the periodic table of topological insulators and superconductors has been derived by establishing the loop sequence of the corresponding classifying spaces. In our approach, each classifying spaces has been regarded as a fiber bundle defined on one point, following that the loop relationship between the classifying spaces in the same symmetric class has been built and proved. Meanwhile, the loop sequence between the classifying spaces with the same spatial dimension has also been developed based on the minimal geodesic approximation. Finally, by building the loop sequence for general dimensions and symmetric classes, a complete homotopic understanding about the whole periodic table of any classifying spaces is achieved. Our approach provides a unified way to interpret the topological relationship between any free-fermion systems.
Hodge classes of Chern character forms on compact K\"ahler manifolds

In this paper we show that every rational cohomology class of type $(p,p)$ on a compact K\"ahler manifold can be representated as a differential $(p,p)$-form given by an explicit formula involving a \v{C}ech cocycle. First we represent Chern characters of smooth vector bundles by \v{C}ech cocycles with values in the sheaf of differential forms. We then consider the behavior of these cocycles with respect to the Hodge structure on cohomology when the base manifold is compact K\"ahler.
A gluing theorem for the Kapustin–Witten equations with a Nahm pole

In the present paper, we establish a gluing construction for the Nahm pole solutions to the Kapustin–Witten equations over manifolds with boundaries and cylindrical ends. Given two Nahm pole solutions with some convergence assumptions on the cylindrical ends, we prove that there exists an obstruction class for gluing the two solutions together along the cylindrical end. In addition, we establish a local Kuranishi model for this gluing picture. As an application, we show that over any compact 4‐manifold with S3 or T3 boundary, there exists a Nahm pole solution to the obstruction perturbed Kapustin–Witten equations. This is also the case for a 4‐manifold with hyperbolic boundary under some topological assumptions.
Phase field modelling of surfactants in multi-phase flow

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions.