Miracle-dz/UniFAR-FTUs huggingface dataset:
Efficient Registration-Based Encryption

Registration-based encryption (RBE) was recently introduced as an alternative to identity-based encryption (IBE), to resolve the key-escrow problem: In RBE, the trusted authority is substituted with a weaker entity, called the key curator, who has no knowledge of any secret key. Users generate keys on their own and then publicly register their identities and their corresponding public keys to the key curator. RBE is a promising alternative to IBE, retaining many of its advantages while removing the key-escrow problem, the major drawback of IBE. Unfortunately, all existing constructions of RBE use cryptographic schemes in a non black-box way, which makes them prohibitively expensive. It has been estimated that the size of an RBE ciphertext would be in the order of terabytes (though no RBE has even been implemented). In this work, we propose a new approach to construct RBE, from standard assumptions in bilinear groups. Our scheme is black-box and it is concretely highly efficient-a ciphertext is 914 bytes. To substantiate this claim, we implemented a prototype of our scheme and we show that it scales to millions of users. The public parameters of the scheme are on the order of kilobytes. The most expensive operation (registration) takes at most a handful of seconds, whereas the encryption and decryption runtimes are on the order of milliseconds. This is the first-ever implementation of an RBE scheme and demonstrates that the practical deployment of RBE is already possible with today's hardware.
Adapted pairs and Weierstrass sections

Adapted pairs and Weierstrass sections are central to the invariant theory associated to the action of an algebraic Lie algebra a on a finite dimensional vector space X. In this a need not be a semisimple Lie algebra. Here their general properties are described particularly when a is the canonical truncation of a biparabolic subalgebra of a simple Lie algebra and X is the dual of a.
The harmonic map heat flow on conic
 manifolds

In this article, we study the the harmonic map heat flow from a manifold with conic singularities to a closed manifold. In particular, we have proved the short time existence and uniqueness of solutions as well as the existence of global solutions into manifolds with nonpositive sectional curvature. These results are established in virtue of the maximal regularity theory on manifolds with conic singularities.
Following the evolution of metastable glassy states under external perturbations : compression and shear-strain

We consider the adiabatic evolution of glassy states under external perturbations. Although the formalism we use is very general, we focus here on infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i. e. compression or (volume preserving) shear-strain, and we compute the response of glassy states to such perturbations: pressure and shear-stress. We find that both quantities over shoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation. We then study the high-pressure and high-strain regime beyond the Gardner transition.
Core-crust transition pressure for relativistic slowly rotating neutron stars

We study the influence of core-crust transition pressure changes on the general dynamical properties of neutron star configurations. First we study the matching conditions in core-crust transition pressure region, where phase transitions in the equation of state causes energy density jumps. Then using a surface crust approximation, we can construct configurations where the matter is described by the equation of state of the core of the star and the core-crust transition pressure. We will consider neutron stars in the slow rotation limit, considering perturbation theory up to second order in the angular velocity so that the deformation of the star is also taken into account. The junction determines the parameters of the star such as total mass, angular and quadrupolar momentum.
Optics clues to pairing glues in high T c cuprates

We analyze optical spectra of high temperature superconductors using a minimal model of electrons coupled to bosons. We consider the marginal Fermi liquid theory and the spin fluctuation theory, as well as a histogram representation of the bosonic spectral density. We find that the two theories can both be used to describe the experimental data provided that we allow for an additional scattering channel with an energy of 55 meV.
Reality and Computation in Schubert Calculus

The Mukhin-Tarasov-Varchenko Theorem (previously the Shapiro Conjecture) asserts that a Schubert problem has all solutions distinct and real if the Schubert varieties involved osculate a rational normal curve at real points. This sparked interest in real osculating Schubert calculus, and computations played a large role in developing the surrounding theory. We uncover generalizations of the Mukhin-Tarasov-Varchenko Theorem, proving them when possible. We also improve the state of the art of computationally solving Schubert problems, allowing us to more effectively study ill-understood phenomena in Schubert calculus. We use supercomputers to methodically solve real osculating instances of Schubert problems. By studying over 300 million instances of over 700 Schubert problems, we amass data significant enough to reveal possible generalizations of the Mukhin-Tarasov-Varchenko Theorem and compelling enough to support our conjectures. Combining algebraic geometry and combinatorics, we prove some of these conjectures. To improve the efficiency of solving Schubert problems, we reformulate an instance of a Schubert problem as the solution set to a square system of equations in a higher-dimensional space. During our investigation, we found the number of real solutions to an instance of a symmetrically defined Schubert problem is congruent modulo four to the number of complex solutions. We prove this congruence, giving a new invariant in enumerative real algebraic geometry. We also discovered a family of Schubert problems whose number of real solutions to a real osculating instance has a lower bound depending only on the number of defining flags with real osculation points.
Weakly polynomial efficient minimization of a non-convex quadratic function with logarithmic barriers in a trust-region

We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance of the considered problem. We lay out how solutions of this problem can be used as efficient step-directions in solution methods for nonlinear programming. We present a theoretical algorithm for solving the problem. We show that this algorithm has weak polynomial time-complexity. A practical method is under development. In the outlook we discuss how the given method can be accelerated for better practical performance. We also lay out where the difficulties live when trying to formulate an accelerated primal-dual variant.
Relativistic quantum mechanics and relativistic entanglement in the rest-frame instant form of dynamics

A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics, where the world-lines of the particles are parametrized in terms of the Fokker-Pryce center of inertia and of Wigner-covariant relative 3-coordinates inside the instantaneous Wigner 3-spaces, and where there is a decoupled (non-covariant and non-local) canonical relativistic center of mass. This approach: (a) allows us to make a consistent quantization in every inertial frame; (b) leads to a description of both bound and scattering states; (c) offers new insights on the relativistic localization problem; (d) leads to a non-relativistic limit with a Hamilton-Jacobi treatment of the Newton center of mass; (e) clarifies non-local aspects (spatial non-separability) of relativistic entanglement connected with Lorentz signature and not present in its non-relativistic treatment.
On the early history of moduli and Teichm{ü}ller spaces

We survey some major contributions to Riemann's moduli space and Teichm{\"u}ller space. Our report has a historical character, but the stress is on the chain of mathematical ideas. We start with the introduction of Riemann surfaces, and we end with the discovery of some of the basic structures of Riemann's moduli space and Teichm{\"u}ller space. We point out several facts which seem to be unknown to many algebraic geometers and analysts working in the theory. The period we are interested in starts with Riemann, in 1851, and ends in the early 1960s, when Ahlfors and Bers confirmed that Teichm{\"u}ller's results were correct.This paper was written for the book "Lipman Bers, a life in Mathematics," edited by Linda Keen , Irwin Kra and Rubi Rodriguez (Amercian Mathematical Society, 2015). It is dedicated to the memory of Lipman Bers who was above all a complex analyst and spent a large part of his life and energy working on the analytic structure of Teichm{\"u}ller space. His work on analysis is nevertheless inseparable from geometry and topology. In this survey, we highlight the relations and the logical dependence between this work and the works of Riemann, Poincar{\'e}, Klein, Brouwer, Siegel, Teichm{\"u}ller, Weil, Grothendieck and others. We explain the motivation behind the ideas. In doing so, we point out several facts which seem to be unknown to many Teichm{\"u}ller theorists.
An RBF-FD polynomial method based on polyharmonic splines for the Navier-Stokes equations: Comparisons on different node layouts

Polyharmonic spline (PHS) radial basis functions (RBFs) are used together with polynomials to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial discretization of the compressible Navier-Stokes equations at low Mach number, relevant to atmospheric flows. Test cases are taken from the numerical weather prediction community and solved on bounded domains. Thus, attention is given on how to handle boundaries with the RBF-FD method, as well as a novel implementation for the presented approach. Comparisons are done on Cartesian, hexagonal, and quasi-uniformly scattered node layouts. Since RBFs are independent of a coordinate system (and only depend on the distance between nodes), changing the node layout amounts to changing one line of code. In addition, consideration and guidelines are given on PHS order, polynomial degree and stencil size. The main advantages of the present method are: 1) capturing the basic physics of the problem surprisingly well, even at very coarse resolutions, 2) high-order accuracy without the need of tuning a shape parameter, and 3) the inclusion of polynomials eliminates stagnation (saturation) errors.
Essentially Finite Vector Bundles on Normal Pseudo-Proper Algebraic Stacks

Let $X$ be a normal, connected and projective variety over an algebraically closed field $k$. It is known that a vector bundle $V$ on $X$ is essentially finite if and only if it is trivialized by a proper surjective morphism $f:Y\to X$. In this paper we introduce a different approach to this problem which allows to extend the results to normal, connected and strongly pseudo-proper algebraic stack of finite type over an arbitrary field $k$.
Spectral parameter power series for arbitrary order linear differential equations

Let L be the n‐th order linear differential operator Ly=ϕ0y(n)+ϕ1y(n−1)+⋯+ϕny with variable coefficients. A representation is given for n linearly independent solutions of Ly=λry as power series in λ, generalizing the SPPS (spectral parameter power series) solution that has been previously developed for n=2. The coefficient functions in these series are obtained by recursively iterating a simple integration process, beginning with a solution system for λ=0. It is shown how to obtain such an initializing system working upwards from equations of lower order. The values of the successive derivatives of the power series solutions at the basepoint of integration are given, which provides a technique for numerical solution of n‐th order initial value problems and spectral problems.
The Broucke-H\'enon orbit and the Schubart Orbit in the planar three-body problem with equal masses

In this paper, we study the variational properties of two special orbits: the Schubart orbit and the Broucke-H\'{e}non orbit. We show that under an appropriate topological constraint, the action minimizer must be either the Schubart orbit or the Broucke-H\'{e}non orbit. One of the main challenges is to prove that the Schubart orbit coincides with the action minimizer connecting a collinear configuration with a binary collision and an isosceles configuration. A new geometric argument is introduced to overcome this challenge.
Statistical properties of the energy exchanged between two heat baths coupled by thermal fluctuations

We study both experimentally and theoretically the statistical properties of the energy exchanged between two electrical conductors, kept at different temperatures by two different heat reservoirs, and coupled by the electrical thermal noise. Such a system is ruled by the same equations as two Brownian particles kept at different temperatures and coupled by an elastic force. We measure the heat flowing between the two reservoirs and the thermodynamic work done by one part of the system on the other. We show that these quantities exhibit a long-time fluctuation theorem. Furthermore, we evaluate the fluctuating entropy, which satisfies a conservation law. These experimental results are fully justified by the theoretical analysis. Our results give more insight into the energy transfer in the famous Feynman ratchet, widely studied theoretically but never in an experiment.
Male and female voles do not differ in their assessments of predation risk 1

: A forager’s willingness to trade off safety for food varies with its energetic state. Animals in a low energetic state should accept higher risk than animals with larger energy reserves. In mammals, energy expenditure by females on gestation and lactation may exceed the relatively low cost of sperm production by males. It follows, if reproductive costs are indeed higher for females than for males, that reproductive females may be more likely than males to trade safety for food. Thus, we evaluated the use of safe versus risky foraging patches by male and female meadow voles using putatively safe and risky habitats. We also used behavioural trials to assess whether sexual differences in personality could account for any differences in patch use. Voles preferred to forage in safe patches over risky ones. There was no difference between male and female voles, or between reproductive and non-reproductive individuals, in their respective use of safe versus risky foraging patches. Personality also had no effect on patch choice. The results are consistent with recent studies on other species that have failed to find differences in reproductive costs between the sexes. Experiments on foraging behaviour might thus provide simple and repeatable tests for sexual differences and similarities in reproductive costs. aussi effectué des tests comportementaux pour évaluer si des différences de personnalité reliées au sexe pourraient entraîner une utilisation différente des parcelles. Tous les campagnols ont préféré s'alimenter dans des parcelles sécuritaires plutôt que risquées. Il n'y avait aucune différence entre les sexes ou entre des individus reproducteurs ou non dans leur utilisation de parcelles d'alimentation sécuritaires ou risquées. La personnalité n'avait pas non plus d'effet sur le choix du type de parcelle. Ces résultats sont compatibles avec des études récentes sur d'autres espèces qui n'ont pas trouvé de différence entre les sexes dans les dépenses énergétiques liées à la reproduction. Des expériences sur le comportement de quête alimentaire peuvent donc constituer des tests simples qu’il est possible de répéter dans le but d’évaluer les différences et ressemblances entre les sexes dans les dépenses liées à la reproduction.
Diagrammatics for SU(2) invariant matrix product states

We report on a systematic implementation of su(2) invariance for matrix product states (MPS) with concrete computations cast in a diagrammatic language. As an application we present a variational MPS study of a spin-1/2 quantum chain. For efficient computations, we make systematic use of the su(2) symmetry at all steps of the calculations: (i) the matrix space is set up as a direct sum of irreducible representations, (ii) the local matrices with state-valued entries are set up as superposition of su(2) singlet operators, (iii) products of operators are evaluated algebraically by making use of identities for 3j and 6j symbols. The remaining numerical computations like the diagonalization of the associated transfer matrix and the minimization of the energy expectation value are done in spaces free of symmetry degeneracies. The energy expectation value is a strict upper bound of the true ground-state energy and yields definite conclusions about the accuracy of density-matrix renormalization group results reported in the literature. Furthermore, we present explicit results with accuracy better than 10−4 for nearest- and next-nearest-neighbour spin correlators and for general dimer–dimer correlators in the thermodynamical limit of the spin- Heisenberg chain with frustration.
Hybrid Power Management and Control of PV Systems with Hybrid Energy Storage

: Photovoltaic (PV) technology is widely used in many applications. However, the PV system depends on the temperature and the amount of solar radiation. The energy produced by the PV system can have a surplus or a shortfall of electric power at demand response (DR), resulting in either loss or no energy use or service interruptions. The problem of discontinuous generation is overcome by crossbreeding. The study investigates the design and energy management of a grid-connected residential PV system with a battery and super-capacitor. The battery, super-capacitor, and PVs terminals are connected to the 311 VDC common bus using three DC-DC converters in a parallel structure. Batteries and super-capacitors are subject to strict stabilisation in boost and run modes, resulting in more precise tuning of the controller. In addition to creating a reference output current to synchronise the hybrid system with the grid using a phase closed loop (PLL), the proposed system provides and manages solar energy and an ON/OFF grid storage system, as well as a two-way connection to enable the homeowner to share the power with the grid. The proposed model was designed, simulated, and tested using MATLAB software.
Saturation of a spin-1/2 particle by generalized local control

We show how to apply a generalization of local control design to the problem of the saturation of a spin-1/2 particle by magnetic fields in nuclear magnetic resonance. The generalization of local or Lyapunov control arises from the fact that the derivative of the Lyapunov function does not depend explicitly on the control field. The second derivative is used to determine the local control field. We compare the efficiency of this approach with that of the time-optimal solution that has recently been derived using geometric methods.
Movement Disorder in Demyelinating Disease: Tracing the Charcot's Foot Print

Movement disorders may be one of the neurological manifestations of demyelinating disorders. They can manifest in Parkinsonism or a wide spectrum of hyperkinetic movement disorders including tremor, paroxysmal dyskinesia, dystonia, chorea, and ballism. Some of these disorders occur during an acute episode of demyelination, whereas others can develop later or even may precede the onset of the demyelinating disorders. The pathophysiology of movement disorders in demyelination is complex and the current evidence indicates a wide involvement of different brain networks and spinal cord. Treatment is mainly symptomatic and oral pharmacological agents are the mainstay of the management. Botulinum toxin and neurosurgical interventions may be required in selected patients.
Finding perfect matchings in random regular graphs in linear time

In a seminal paper on finding large matchings in sparse random graphs, Karp and Sipser proposed two algorithms for this task. The second algorithm has been intensely studied, but due to technical difficulties, the first algorithm has received less attention. Empirical results suggest that the first algorithm is superior. In this paper we analyze an adapted version of the first algorithm, the Reduce-Construct algorithm. We show that the Reduce-Construct algorithm finds a maximum matching in random $k=O(1)$-regular graphs in linear time in expectation, as opposed to $O(n^{3/2})$ time for the worst-case.
Revised Algorithmic Approach to Differentiate Between Nonspecific and Specific Etiologies of Chronic Terminal Ileitis

INTRODUCTION: Chronic isolated terminal ileitis (TI) may be seen in Crohn's disease (CD) and intestinal tuberculosis (ITB) in addition to other etiologies that may be managed symptomatically. We developed a revised algorithm to distinguish patients with a specific etiology from a nonspecific etiology. METHODS: Patients with chronic isolated TI followed up from 2007 to 2022 were retrospectively reviewed. A specific (ITB or CD) diagnosis was made based on standardized criteria, and other relevant data were collected. Using this cohort, validation of a previously suggested algorithm was conducted. Furthermore, based on the results of a univariate analysis, a multivariate analysis with bootstrap validation was used to develop a revised algorithm. RESULTS: We included 153 patients (mean age 36.9 ± 14.6 years, males—70%, median duration—1.5 years, range: 0–20 years) with chronic isolated TI of whom 109 (71.2%) received a specific diagnosis (CD-69, ITB-40). On multivariate regression and validation statistics with a combination of clinical, laboratory, radiological, and colonoscopic findings, an optimism corrected c-statistic of 0.975 and 0.958 was obtained with and without histopathological findings, respectively. Revised algorithm, based on these, showed sensitivity, specificity, positive and negative predictive values, and overall accuracy of 98.2% (95% CI: 93.5–99.8), 75.0% (95% CI: 59.7–86.8), 90.7% (95% CI: 85.4–94.2), 94.3% (95% CI: 80.5–98.5) and 91.5%(95% CI:85.9–95.4), respectively. This was more sensitive and specific than the previous algorithm (accuracy 83.9%, sensitivity 95.5%, and specificity 54.6%). DISCUSSION: We developed a revised algorithm and a multimodality approach to stratify patients with chronic isolated TI into specific and nonspecific etiologies with an excellent diagnostic accuracy, which could potentially avoid missed diagnosis and unnecessary side effects of treatment.
Revival‐collapse phenomenon in the quadrature squeezing of the multiphoton Jaynes‐Cummings model with the binomial states

In this paper we study the interaction between a two‐level atom and a quantized single‐mode field, namely, the Jaynes‐Cummings model (JCM). The field and the atom are initially prepared in the binomial state and the excited atomic state, respectively. For this system we prove that the revival‐collapse phenomenon exhibited in the atomic inversion of the standard JCM can be numerically (naturally) manifested in the evolution of the squeezing factor of the three‐photon (standard) JCM provided that the initial photon‐number distribution of the radiation field has a smooth envelope.