Miracle-dz/UniFAR-FTUs huggingface dataset:
Wigner crystallization in a single and bilayer graphene

We study the possibility of Wigner crystallization in both single- and and bi-layer graphene using a real space tight binding model. In addition to verifying our earlier prediction for single layer graphene, we predict that the bilayer graphene can undergo a Wigner crystal transition at low enough carrier density thus offering a possibility of tunable and bipolar Wigner crystal. We find that aside from the Coulomb interaction of the carriers of two layers that stabilizes the charge ordered state, so does the inter layer coupling.
Orientation and rupture of fractal colloidal gels during start-up of steady shear flow

The transient structural evolution of polystyrene colloidal gels with fractal structure is quantified during start-up of steady shear flow by time-resolved small-angle light scattering and rheometry. Three distinct regimes are identified in the velocity-gradient plane: structural orientation, network breakup, and cluster densification. Structural anisotropy in the first regime is a universal function of applied strain. Flow cessation in this regime shows a lack of structural relaxation for Pe⪡1, where Pe is the Peclet number. In the second regime, the anisotropy attains a maximum value before monotonically decreasing. The volume fraction dependence of the critical strain for maximum anisotropy follows the scaling: 1+0. 6γc,r∼ϕ(1−x)(3−D). Here x and D are the backbone and cluster fractal dimensions, respectively. This scaling agrees with the simple model of a gel network that ruptures after the cluster backbone is extended affinely to its full length. Rheological measurements demonstrate that the maximum an.
Axial Cross Attention Meets CNN: Bibranch Fusion Network for Change Detection

In the previous years, vision transformer has demonstrated a global information extraction capability in the field of computer vision that convolutional neural network (CNN) lacks. Due to the lack of inductive bias in vision transformer, it requires a large amount of data to support its training. In the field of remote sensing, it costs a lot to obtain a significant number of high-resolution remote sensing images. Most existing change detection networks based on deep learning rely heavily on the CNN, which cannot effectively utilize the long-distance dependence between pixels for difference discrimination. Therefore, this work aims to use a high-performance vision transformer to conduct change detection research with limited data. A bibranch fusion network based on axial cross attention (ACABFNet) is proposed. The network extracts local and global information of images through the CNN branch and transformer branch, respectively, and then, fuses local and global features by the bidirectional fusion approach. In the upsampling stage, similar feature information and difference feature information of the two branches are explicitly generated by feature addition and feature subtraction. Considering that the self-attention mechanism is not efficient enough for global attention over small datasets, we propose the axial cross attention. First, global attention along the height and width dimensions of images is performed respectively, and then cross attention is used to fuse the global feature information along two dimensions. Compared with the original self-attention, the structure is more graphics processing unit friendly and efficient. Experimental results on three datasets reveal that the ACABFNet outperforms existing change detection algorithms.
Structures riemanniennes L^p et K-homologie

We construct analytically the signature operator for a new family of topological manifolds. This family contains the quasi-conformal manifolds and the topological manifolds modeled on germs of homeomorphisms of R^n possessing a derivative which is in L^p, with p > n(n+1)/2. We obtain an unbounded Fredholm module which defines a class in the K-homology of the manifold, the Chern character of which is the Hirzebruch polynomial in the Pontrjagin classes of the manifold. This generalizes previous works of N. Teleman for Lipschitz manifolds and of A. Connes, N. Teleman and D. Sullivan for quasi-conformal manifolds of even dimension.
Notes on genus one real Gromov-Witten invariants

In this paper, we propose a definition of genus one real Gromov-Witten invariants for certain symplectic manifolds with real a structure, including Calabi-Yau threefolds, and use equivariant localization to calculate certain genus one real invariants of the projective space. For this definition, we combine three moduli spaces corresponding to three possible types of involutions on a symplectic torus, by gluing them along common boundaries, to get a moduli space without codimension-one boundary and then study orientation of the total space. Modulo a technical conjectural lemma, we can prove that the result is an invariant of the corresponding real symplectic manifold. In the aforementioned example, our main motivation is to show that the physicists expectation for the existence of separate Annulus, Mobius, and Klein bottle invariants may not always be true.
What is the best index of detectability?

Various indices which have been proposed as measures of detectability (for unequal variance normal distributions of signal and nonsignal) are discussed. It is argued that the best measure is an index, denoted by $d_a$, which is defined as $\sqrt(2)$ times the orthonormal distance from the origin of the normal deviate graph to the straight line receiver operating characteristic. It is shown that $d_a/\sqrt(2)$ is equal to $z(A)$, thenormal transform of the area under the receiver operating characteristic curve, $P(A)$. The effect of changes in the variance of the signal distribution on $d_a$ and competing indices is described. "Nonparametric" indices, appropriate when normality is not assumed, are also discussed and an index based on the difference distribution formed from two rating distributions is proposed. This index, also, is related to the area under the receiver operating characteristic curve. The sampling variability of $z(A)$ was investigated by computer simulation and found to be generally lower than the theoretical sampling variability. Some simplifications are proposed to the conclusions drawn from an earlier simulation.
Wold decompositions for operators close to isometries

In Bergman and Dirichlet spaces, the shift operator is not an isometry, but it is a left invertible operator. In this paper we give conditions on the left invertible operators such that a operator version, in the sense of Rosenblum and Rovnyak, of the Wold decomposition to take place.
Riemann's Zeta Function: The alternating Xi-Function Xia(s)

As well known, the study of Riemanns zeta function {\zeta}(s) involves the related entire function {\xi}(s). A close relative of {\zeta}(s) is the alternating zeta function {\eta}(s). Similar to {\zeta}(s), also {\eta}(s) has a corresponding entire function {\xi}_a (s). After establishing its definition and a related functional equation, formulas based on incomplete gamma functions are worked out, allowing to numerically evaluate {\xi}_a (s). Examples verifying the obtained formulas are included.
Non-linear dynamics of semiconductor superlattices

In the last decade, non-linear dynamical transport in semiconductor superlattices (SLs) has witnessed significant progress in theoretical descriptions as well as in experimentally observed non-linear phenomena. However, until now, a clear distinction between non-linear transport in strongly and weakly coupled SLs was missing, although it is necessary to provide a detailed description of the observed phenomena. In this review, strongly coupled SLs are described by spatially continuous equations and display self-sustained current oscillations due to the periodic motion of a charge dipole as in the Gunn effect for bulk semiconductors. In contrast, weakly coupled SLs have to be described by spatially discrete equations. Therefore, weakly coupled SLs exhibit a more complex dynamical behaviour than strongly coupled ones, which includes the formation of stationary electric field domains, pinning or propagation of domain walls consisting of a charge monopole, switching between stationary domains, self-sustained current oscillations due to the recycling motion of a charge monopole and chaos. This review summarizes the existing theories and the experimentally observed non-linear phenomena for both types of semiconductor SLs.
A condition analysis of the weighted linear least squares problem using dual norms

Abstract In this paper, based on the theory of adjoint operators and dual norms, we define condition numbers for a linear solution function of the weighted linear least squares problem. The explicit expressions of the normwise and componentwise condition numbers derived in this paper can be computed at low cost when the dimension of the linear function is low due to dual operator theory. Moreover, we use the augmented system to perform a componentwise perturbation analysis of the solution and residual of the weighted linear least squares problems. We also propose two efficient condition number estimators. Our numerical experiments demonstrate that our condition numbers give accurate perturbation bounds and can reveal the conditioning of individual components of the solution. Our condition number estimators are accurate as well as efficient.
Co-production models with random functionality yields

Production systems with random functionality yields and downward substitutable demand are modeled and investigated. Such systems arise frequently in the electronics and petrochemical industries. We analyze two single-period models. The first models a single production process in which the total yield of usable products is uncertain; furthermore the realized usable products are of two grades, higher and lower, and the portions of each grade products are also uncertain. Demand for lower-grade products can be met, if necessary, by higher-grade units. The second model we analyze has two parallel production processes: one is as in die previous model; the other is attempting to produce lower-grade products only, but their yield is random. In both single-process and two-process scenarios the relative magnitudes of the salvage values of the two product grades lead to somewhat different models that need to be analyzed separately. We prove that all the expected profit functions are concave (jointly concave), and de.
Regularity estimates for nonlocal Schrödinger equations

We prove H\"older regularity estimates up to the boundary for weak solutions $u$ to nonlocal Schr\"odinger equations subject to exterior Dirichlet conditions in an open set $\Omega\subset \mathbb{R}^N$. The class of nonlocal operators considered here are defined, via Dirichlet forms, by kernels $K(x,y)$ bounded from above and below by $|x-y|^{N+2s}$, with $s\in (0,1)$. The entries in the equations are in some Morrey spaces and the underline domain $\Omega$ satisfies some mild regularity assumptions. In the particular case of the fractional Laplacian, our results are new. When $K$ defines a nonlocal operator with sufficiently regular coefficients, we obtain H\"older estimates, up to the boundary of $ \Omega$, for $u$ and the ratio $u/d^s$, with $d(x)=\textrm{dist}(x,\mathbb{R}^N\setminus\Omega)$. If the kernel $K$ defines a nonlocal operator with H\"older continuous coefficients and the entries are H\"older continuous, we obtain interior $C^{2s+\beta}$ regularity estimates of the weak solutions $u$. Our argument is based on blow-up analysis and compact Sobolev embedding.
Computational experience with the solution of the matrix Lyapunov equation

This correspondence presents a comparative study of three methods for the numerical solution of the matrix Lyapunov equation. The test case is a 24th-order system with highly underdamped eigenvalues and a rather high degree of stiffness. The conclusions favor a method by Bartels and Stewart based on a reduction to Schur form of the A matrix.
Scaling Law of the Hausdorff Measure

The scaling properties of length, area and volume are well known. On magnification by a factor λ, the length of a curve is multiplied by λ, the area of a plane region is multiplied by λ and the volume of a 3-dimensional object is multiplied by λ. It is well known that the scaling factor of s-dimensional Hausdorff measure is λ [3]. Such scaling properties are fundamental to the theory of fractals . Especially, the authors in [2], [4] have proved that the scaling property of the Hausdorff measureH on R holds for a continuous increasing function h defined on R = {x ∈ R|x > 0} with h(0) = 0 such that h is strictly concave down on a right neighborhood of 0
Design optimization of three‐phase energy efficient induction motor using adaptive bacterial foraging algorithm

Purpose – The purpose of this paper is to present the application of an adaptive bacterial foraging (BF) algorithm for the design optimization of an energy efficient induction motor.Design/methodology/approach – The induction motor design problem is formulated as a mixed integer nonlinear optimization problem. A set of nine independent variables is selected, and to make the machine feasible and practically acceptable, six constraints are imposed on the design. Two different objective functions are considered, namely, the annual active material cost, and the sum of the annual active material cost, annual cost of the active power loss of the motor and annual energy cost required to supply such power loss. A new adaptive BF algorithm is used for solving the optimization problem. A generic penalty function method, which does not require any penalty coefficient, is employed for constraint handling.Findings – The adaptive BF algorithm is validated for two sample motors and benchmarked with the genetic algorithm.
DIFFERENTIAL OPERATORS ON $G/U$ AND THE AFFINE GRASSMANNIAN

We describe the equivariant cohomology of cofibers of spherical perverse sheaves on the affine Grassmannian of a reductive algebraic group in terms of the geometry of the Langlands dual group. In fact we give two equivalent descriptions: one in terms of $\mathscr{D}$-modules of the basic affine space, and one in terms of intertwining operators for universal Verma modules. We also construct natural collections of isomorphisms parameterized by the Weyl group in these three contexts, and prove that they are compatible with our isomorphisms. As applications we reprove some results of the first author and of Braverman and Finkelberg.
A Two-Step Pre-Processing for Semidefinite Programming

In semidefinite programming (SDP), a number of pre-processing techniques have been developed, including procedures based on chordal decomposition, which exploit sparsity in the semidefinite program in order to reduce the dimension of individual constraints, and procedures based on facial reduction, which reduces the dimension of the problem by removing redundant rows and columns. So far, these have been studied in isolation. We show that these techniques are, in fact, complementary. In computational experiments, we show that a two-step pre-processing followed by a standard interior-point method outperforms the interior point method, with or without either of the pre-processing techniques, by a considerable margin.
Evolution of flat-plate wakes in sink flow

Evolution of flat-plate wakes in sink flow has been studied both analytically and experimentally. For such wakes, a similarity solution is derived which considers simultaneous presence of both laminar and turbulent stresses inside the wake. This solution utilizes an additional Reynolds-stress term which represents the fluctuations similar to those in wall-bounded flows, accounting for the fluctuations originating from the plate boundary layer. In this solution, it is shown that the total stress, the sum of laminar and Reynolds shear stresses, becomes self-similar. To investigate the accuracy of the analytical results, the wake of a flat plate located at the centreline of a planar contraction is studied using hot-wire anemometry. Wakes of both tapered and blunt edges are considered. The length of the plates and the flow acceleration number K = 6.25 × 10−6 are chosen such that the boundary-layer profiles at the plate edge approach the self-similar laminar solution of Pohlhausen (Z. Angew. Math. Mech., vol. 1, 1921, p. 252). A short plate in which the boundary layer at the edge does not fully relaminarize is also considered. The development of the turbulent diffusivity used in the analysis is determined empirically for each experimental case. We have shown that the obtained similarity solutions, accounting also for the initial conditions in each case, generally agree well with the experimental results even in the near field. The results also show that the mean velocity of the transitional wake behind a tapered edge becomes self-similar almost immediately downstream of the edge.
Mukai flops and derived categories

In this note, we shall prove that two smooth projective varieties of dim 2n connected by a Mukai flop have equivalent bounded derived categories. More precisely, let $\phi : X - - \to X^+$ be a Mukai flop with centers $Y \subset X$ and $Y^+ \subset X^+$. In our case, the natural fuctor $\Phi : D(X) \to D(X^+)$ defined by the graph of $\phi$ is not fully faithful. Instead, let $X \to {\bar X}$ and $X^+ \to {\bar X}$ be the birational contraction maps of the centers, and put ${\hat X} := X \times_{{\bar X} X^+$. Then ${\hat X}$ is a normal crossing variety with two irreducible components. This ${\hat X}$ defines a functor $\Psi : D(X) \to D(X^+)$. We shall prove that this $\Psi$ is an equivalence. Recently, Wierzba and Wisniewski have announced that two birationally equivalent, complex projective symplectic 4-folds are connected by a finite sequence of Mukai flops. Our result with this shows that $D(X)$ is a birational invariant for complex projective symplectic 4-folds.
Anosov representations and dominated splittings

We provide a link between Anosov representations introduced by Labourie and dominated splitting of linear cocycles. This allows us to obtain equivalent characterizations for Anosov representations and to recover recent results due to Gueritaud-Guichard-Kassel-Wienhard and Kapovich-Leeb-Porti by different methods. We also give characterizations in terms of multicones and cone-types inspired in the work of Avila-Bochi-Yoccoz and Bochi-Gourmelon. Finally we provide a new proof of the higher rank Morse Lemma of Kapovich-Leeb-Porti.
Modelling Time Series of Counts in Epidemiology

We review generalized dynamic models for time series of count data. Usually temporal counts are modelled as following a Poisson distribution, and a transformation of the mean depends on parameters which evolve smoothly with time. We generalize the usual dynamic Poisson model by considering continuous mixtures of the Poisson distribution. We consider Poisson‐gamma and Poisson‐log‐normal mixture models. These models have a parameter for each time t which captures possible extra‐variation present in the data. If the time interval between observations is short, many observed zeros might result. We also propose zero inflated versions of the models mentioned above. In epidemiology, when a count is equal to zero, one does not know if the disease is present or not. Our model has a parameter which provides the probability of presence of the disease given no cases were observed. We rely on the Bayesian paradigm to obtain estimates of the parameters of interest, and discuss numerical methods to obtain samples from the resultant posterior distribution. We fit the proposed models to artificial data sets and also to a weekly time series of registered number of cases of dengue fever in a district of the city of Rio de Janeiro, Brazil, during 2001 and 2002.
Deformations of hypercomplex structures related to Heisenberg groups

Let $X$ be a compact quotient of the product of the real Heisenberg group $H_{4m+1}$ of dimension $4m+1$ and the 3-dimensional real Euclidean space $\bR^3$. A left invariant hypercomplex structure on $H_{4m+1}\times \bR^3$ descends onto the compact quotient $X$. The space $X$ is a hyperholomorphic fibration of 4-tori over a $4m$-torus. We calculate the parameter space and obstructions to deformations of this hypercomplex structure on $X$. Using our calculations we show that all small deformations generate invariant hypercomplex structures on $X$ but not all of them arise from deformations of the lattice. This is in contrast to the deformations on the $4m$-torus.
The search for the magnetic precursor of C-type shocks in young molecular outflows

The detection of very narrow SiO emission and the higher degree of excitation of the ion fluid compared to the neutral one towards the protostar L1448-mm have been interpreted as signatures of the magnetic precursor of C-shocks. Since this is the only source where these features have been observed together, we carried out a survey to map the J = 2→ 1 and 8→ 7 lines of SiO, and the J = 1→ 0 and 4→ 3 lines of HCO (as the representative ion) and HNC (as the representative neutral species) towards four class 0/I low-mass protostars known to have young outflows (L1448-IRS3, NGC 1333-IRAS 4A/B and SSV 13, VLA 1623 and IRAS 20353). As previously reported, towards L1448-IRS3 and NGC 1333 strong, narrow SiO 2→ 1 is detected, and we also find a velocity component towards each outflow which shows high a HCO 4→ 3/1→ 0 integrated intensity ratio compared to that of HNC. Towards VLA 1623, we find very weak, narrow SiO, and a component that is visible in HCO but not at all in HNC. For IRAS 20353, we find neither narrow SiO nor high HCO 4→ 3/1→ 0 flux ratios. Previous work explained the higher degree of excitation of H13CO+ by the selective excitation of ions by electrons, whose abundance is expected to increase at the precursor stage. Here, however, by considering a range of kinetic temperatures for the gas, we find that it is possible to fit the observations with a single temperature and density, without an increased electron abundance, despite the large differences in 4→ 3/1→ 0 ratio between the two molecules. The high H13CO+ 4→ 3/1→ 0 flux ratios may simply be due to protostellar heating. However, the hypothesis that narrow SiO is formed at the precursor stage of shocks remains plausible, since other explanations require either the presence of shocks with larger dynamical timescales, or predict the narrow SiO to have a larger spatial extent than it appears to have towards the sources L1448-IRS3 and VLA 1623. Larger scale maps of the narrow SiO emission are needed to confirm that it is confined to the regions around protostars (as would be expected in the precursor scenario), and mapping of different ion and neutral species is necessary to confirm whether there are indeed precursor regions surrounding young outflows where the ion and neutral species behave as separate fluids.