Miracle-dz/UniFAR-FTUs huggingface dataset:
Combinatorics of $\gamma$-structures

In this paper we study canonical $\gamma$-structures, a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A $\gamma$-structure is composed by specific building blocks, that have topological genus less than or equal to $\gamma$, where composition means concatenation and nesting of such blocks. Our main result is the derivation of the generating function of $\gamma$-structures via symbolic enumeration using so called irreducible shadows. We furthermore recursively compute the generating polynomials of irreducible shadows of genus $\le \gamma$. $\gamma$-structures are constructed via $\gamma$-matchings. For $1\le \gamma \le 10$, we compute Puiseux-expansions at the unique, dominant singularities, allowing us to derive simple asymptotic formulas for the number of $\gamma$-structures.
More on ghosts in the Dvali-Gabadaze-Porrati model

It is shown by an explicit calculation that the excitations about the self-accelerating cosmological solution of the Dvali-Gabadaze-Porrati model contain a ghost mode. This raises serious doubts about viability of this solution. Our analysis reveals the similarity between the quadratic theory for the perturbations around the self-accelerating universe and an Abelian gauge model with two Stueckelberg fields.
Observer‐based adaptive output‐constrained control design of switched stochastic nonlinear systems with input saturation

In this article, the problem of adaptive fuzzy control for output‐constrained switched stochastic nonlinear systems subject to input saturation is addressed. By employing the trigonometric function mapping method, the constrained systems are transformed into unconstrained ones, and the control goals of the original constrained systems are not affected. Meanwhile, an auxiliary system is established to deal with the issue of input saturation, and an observer is constructed to estimate the unmeasured states. Then, the unknown nonlinear functions in the system are approximated by the fuzzy logic systems (FLSs). Based on the backstepping technique and Lyapunov function method, an output feedback control strategy is designed, where the dynamic surface control technique is applied in the backstepping design process to overcome the issue of a large number of online calculations. The designed controller can guarantee that all the signals of the system satisfy bounded conditions, and the output can track given reference signals within a small error range. Finally, a simulation example is given to verify the effectiveness of the proposed control scheme.
Simulation of Fiber Entanglement by Modeling Vorticity in Water Flow Field

This research developed a model of the hydroentanglement process, based on the first principles of fluid mechanics. This model proceeded from the assumption that fiber entanglement in the hydroentanglement process is proportional to the average vorticity in the fiberweb. Two-dimensional simulations of the water flow through the fiberweb and forming surfaces were performed in the plane perpendicular to the machine direction (MD). In these two-dimensional simulations the time-dependent development of the flow field was investigated, and it was found that the vortices induced by the water jets were influenced by the jet pressure and diameter. It was shown that the maximum average vorticity in the fiberweb occurred at a water jet diameter of 0.127 mm which explains why jets of such diameter are commonly used in industry. Three-dimensional simulations were also performed to account for the realistic geometry of the computational domain. The influence of the forming surface permeability was investigated and it was shown that the fiber entanglement increased as the open area of the forming surface decreased.
A sheaf‐theoretic SL(2,C) Floer homology for knots

Using the theory of perverse sheaves of vanishing cycles, we define a homological invariant of knots in three‐manifolds, similar to the three‐manifold invariant constructed by Abouzaid and the second author. We use spaces of SL(2,C) flat connections with fixed holonomy around the meridian of the knot. Thus, our invariant is a sheaf‐theoretic SL(2,C) analogue of the singular knot instanton homology of Kronheimer and Mrowka. We prove that for two‐bridge and torus knots, the SL(2,C) invariant is determined by the l ‐degree of the Â ‐polynomial. However, this is not true in general, as can be shown by considering connected sums of knots.
On closed oriented surfaces in the 3-sphere.

In this paper we study embeddings of $3$-manifolds with connected boundary in $\mathbb S^3$ or, equivalently, embeddings of oriented connected closed surfaces in $\mathbb S^3$. We develop a complete invariant, the fundamental span, for such embeddings, which generalizes the notion of the peripheral system of a knot group. From the fundamental span, several computable invariants are derived, and they are employed to investigate handlebody knots, bi-knotted surfaces and the chirality of a knot. These invariants are capable to distinguish inequivalent handlebody knots and bi-knotted surfaces with homeomorphic complements. Particularly, we obtain an alternative proof of inequivalence of Ishii et al.'s handlebody knots $5_{1}$ and $6_{4}$, and construct an infinite family of pairs of inequivalent bi-knotted surfaces with homeomorphic complements. An interpretation of Fox's invariant in terms of the fundamental span is also discussed; we use it to prove the chirality of $9_{42}$ and $10_{71}$, which are known to be undetectable by the Jones and HOMFLY polynomials.
Holomorphic bundles and scalar difference operators: one-point constructions

Commutative rings of one-dimensional difference operators of rank l>1 and their deformations are effectively constructed. Our analytical constructions are based on the so-called ''Tyurin parameters'' for the stable framed holomorphic vector bundles over algebraic curves of the genus equal to g and Chern number equal to lg. These parameters were heavily used by the present authors already in 1978-80 for the differential operators. Their deformations in the discrete case are governed by the 2D Toda Lattice hierarhy instead of KP. New integrable systems appear here in the case l=2,g=1. The theory of higher rank difference operators is much more rich than the rank one case where only 2-point constructions on the spectral curve were used in the previous literature (i.e. number of 'infinite points'' is equal to 2). One-point constructions appear in this problem for every even rank l=2k. Only in this case commutative rings depend on the functional parameters. Two-point constructions will be studied in the next work: even for higher rank l>1 this case can be solved in Theta-functions. It is not so for one-point constructions with rank l>1.
Presymplectic current and the inverse problem of the calculus of variations

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon, and Lawson [Math. Proc. Cambridge Philos. Soc. 148(01), 159–178 (2010)] and generalizes an older result of Henneaux [Ann. Phys. 140(1), 45–64 (1982)] from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.
Transfer Function Models for Multidimensional Systems with Bounded spatial Domains

Multidimensional (MD) systems describe relations between signals depending on two or more independent variables. They are also called distributed parameter systems, if the independent variables are time and space. The only conventional models for their description are partial differential equations. This is in contrast to onedimensional (lumped parameter) systems, where a variety of different models including transfer functions is used. This paper extends the concept of transfer function models to multidimensional systems with bounded spatial domains, i.e., systems which can be described as initial-boundary-value problems. These transfer function models are useful for system analysis and as a starting point for the derivation of numerically efficient discrete simulation models.
On construction of transmutation operators for perturbed Bessel equations

A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure. New properties of the transmutation kernel are established. A new representation of the regular solution of the perturbed Bessel equation is given presenting a remarkable feature of uniform error bound with respect to the spectral parameter for partial sums of the series. A numerical illustration of application to the solution of Dirichlet spectral problems is presented.
Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms

In this paper, we establish stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms on metric measure spaces under general volume doubling condition. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cutoff Sobolev inequalities, and Poincare inequalities. In particular, we establish the connection between parabolic Harnack inequalities and two-sided heat kernel estimates, as well as with the Holder regularity of parabolic functions for symmetric non-local Dirichlet forms.
A Theoretical and Observational Study of the Radiative Properties of Cirrus: Results from FIRE 1986.

Abstract A two-stream radiative transfer model is used to examine the radiative properties of cirrus clouds and compare simulations with the observations made during the cirrus FIRE IFO. The sensitivity of cirrus cloud radiative properties to altitude and size distribution changes are examined. The net radiative effect of cirrus in the infrared is largely determined by the amount of ice in the cloud and the surface—cloud base temperature difference (and thus altitude). Increases (decreases) of this temperature difference produce a net radiative heating (cooling). Cloud-top solar heating increases (decreases) with increasing (decreasing) altitude as the optical path of the atmosphere above the cloud layer decreases (increases). The impact of varying concentrations of ice particles less than 100 μm in diameter is also examined. The addition of these particles greatly enhances the longwave absorption and shortwave albedo of cirrus clouds in a manner that is spectrally dependent. Model simulations using obser.
A simulation study to examine the sensitivity of the Pettitt test to detect abrupt changes in mean

Abstract The Pettitt test is a non-parametric test that has been used in a number of hydroclimatological studies to detect abrupt changes in the mean of the distribution of the variable of interest. This test is based on the Mann-Whitney two-sample test (rank-based test), and allows the detection of a single shift at an unknown point in time. This test is often used to detect shifts in extremes because of the lack of distributional assumptions. However, the downside of not specifying a distribution is that the Pettitt test may be inefficient in detecting breaks when dealing with extremes. Here we adopt a Monte Carlo approach to examine the sensitivity of the Pettitt test in detecting shifts in the mean under different conditions (location of the break within the series, magnitude of the shift, record length, level of variability in the data, extreme vs non-extreme records, and pre-assigned significance level). These simulation results show that the sensitivity of this test in detecting abrupt changes increases with the increase in the magnitude of the shift and record length. The number of detections is higher when the time series represents the central part of the distribution (e.g. changes in the time series of medians), while the skill decreases as we move toward either low or high extremes (e.g. changes in the time series of maxima). Furthermore, the number of detections decreases as the variability in the data increases. Finally, abrupt changes are more easily detected when they occur toward the center of the time series. Editor D. Koutsoyiannis Associate editor K. Hamed
A local relative trace formula for PGL(2)

Following a scheme inspired by B. Feigon, we describe the spectral side of a local relative trace formula for $G:= PGL(2,\rm E)$ relative to the symmetric subgroup $H:=PGL(2,\rm F)$ where $\rm E/\rm F$ is an unramified quadratic extension of local non archimedean fields of characteristic $0$. This spectral side is given in terms of regularized normalized periods and normalized $C$-functions of Harish-Chandra. Using the geometric side obtained in a more general setting by P. Delorme, P. Harinck and S. Souaifi , we deduce a local relative trace formula for $G$ relative to $H$. We apply our result to invert some orbital integrals.
ROVIBRATIONAL EXCITATION OF HD IN COLLISIONS WITH ATOMIC AND MOLECULAR HYDROGEN

We have computed cross-sections and rate coefficients for rovibrational transitions in HD, induced by collisions with atomic and molecular hydrogen. We employed fully quantum-mechanical methods and the potential of Boothroyd et al. for H–HD, and that of Schwenke for H2–HD. The rate coefficients for vibrational relaxation v=10 of HD are compared with the corresponding values for H2. The influence of vibrationally excited channels on the rate coefficients for rotational transitions within the v=0 vibrational ground state of HD is shown to be small at T=500 K, where T is the kinetic temperature. The rate coefficients, for 100T2000 K, are available from http://ccp7.dur. ac.uk/.
Independence characterization for Wishart and Kummer random matrices.

We generalize the following univariate characterization of the Kummer and Gamma distributions to the cone of symmetric positive definite matrices: let $X$ and $Y$ be independent, non-degenerate random variables valued in $(0, \infty)$, then $U= Y/(1+X)$ and $V = X(1+U)$ are independent if and only if $X$ follows the Kummer distribution and $Y$ follows the the Gamma distribution with appropriate parameters. We solve a related functional equation in the cone of symmetric positive definite matrices, which is our first main result and apply its solution to prove the characterization of Wishart and matrix-Kummer distributions, which is our second main result.
An Analysis of Primal-Dual Algorithms for Discounted Markov Decision Processes

Several well-known algorithms in the field of combinatorial optimization can be interpreted in terms of the primal-dual method for solving linear programs. For example, Dijkstra's algorithm, the Ford-Fulkerson algorithm, and the Hungarian algorithm can all be viewed as the primal-dual method applied to the linear programming formulations of their respective optimization problems. Roughly speaking, successfully applying the primal-dual method to an optimization problem that can be posed as a linear program relies on the ability to find a simple characterization of the optimal solutions to a related linear program, called the `dual of the restricted primal' (DRP). This paper is motivated by the following question: What is the algorithm we obtain if we apply the primal-dual method to a linear programming formulation of a discounted cost Markov decision process? We will first show that several widely-used algorithms for Markov decision processes can be interpreted in terms of the primal-dual method, where the value function is updated with suboptimal solutions to the DRP in each iteration. We then provide the optimal solution to the DRP in closed-form, and present the algorithm that results when using this solution to update the value function in each iteration. Unlike the algorithms obtained from suboptimal DRP updates, this algorithm is guaranteed to yield the optimal value function in a finite number of iterations. Finally, we show that the iterations of the primal-dual algorithm can be interpreted as repeated application of the policy iteration algorithm to a special class of Markov decision processes. When considered alongside recent results characterizing the computational complexity of the policy iteration algorithm, this observation could provide new insights into the computational complexity of solving discounted-cost Markov decision processes.
Gaussian multiplicative chaos through the lens of the 2D Gaussian free field

The aim of this review-style paper is to provide a concise, self-contained and unified presentation of the construction and main properties of Gaussian multiplicative chaos (GMC) measures for log-correlated fields in 2D in the subcritical regime. By considering the case of the 2D Gaussian free field, we review convergence, uniqueness and characterisations of the measures; revisit Kahane's convexity inequalities and existence and scaling of moments; discuss the measurability of the underlying field with respect to the GMC measure and present a KPZ relation for scaling exponents.
Entanglement measures and approximate quantum error correction

It is shown that if the loss of entanglement along a quantum channel is sufficiently small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. Explicit bounds are obtained for the entanglement of formation and the distillable entanglement, and their validity naturally extends to other bipartite entanglement measures in between. Robustness of derived criteria is analyzed and their tightness compared. Finally, as a by-product, we prove a bound quantifying how large the gap between the entanglement of formation and distillable entanglement can be for any given finite dimensional bipartite system, thus providing a sufficient condition for distillability in term of the entanglement of formation.
Fixed points in compactifications and combinatorial counterparts

The Kechris-Pestov-Todorcevic correspondence connects extreme amenability of topological groups with Ramsey properties of classes of finite structures. The purpose of the present paper is to recast it as one of the instances of a more general construction, allowing to show that Ramsey-type statements actually appear as natural combinatorial expressions of the existence of fixed points in certain compactifications of groups, and that similar correspondences in fact exist in various dynamical contexts.
On the pointwise convergence of multiple ergodic averages

It is shown that there exist a subsequence for which the multiple ergodic averages of commuting invertible measure preserving transformations of a Lebesgue probability space converge almost everywhere provided that the maps are weakly mixing with an ergodic extra condition. The proof provides a example of non-singular dynamical system for which the maximal ergodic inequality does not hold. We further get that the non-singular strategy to solve the pointwise convergence of the Furstenberg ergodic averages fails.
WHAT THEORIES EXPLAIN ENTREPRENEURSHIP AS COMPARED TO INNOVATIVE LEADERSHIP?

: Business creation theories were rarely explored with stages that precede the final intention to start a business. Therefore, this paper aimed to examine what factors impact the final decision to start a business and what factors just lead to a more favourable perception of a business opportunity. Several theories recognized by literature like the theory of planned behaviour, traits, cognitive biases, and risk attitudes were tested. Moreover, the explanatory power of these theories to entrepreneurship compared to innovative (leadership) practices was tested. When examining multiple regression models, it was shown that above mentioned theories predict entrepreneurship as well as innovative practices. Model that involved business creation theories predicting opportunity evaluation was significant. Among predictors of opportunity evaluation, it was shown that unrealistic optimism, risk attitudes as well as traits or theory of planned behaviour did contribute to the prediction of opportunity evaluation. When testing multiple regression model of the final decision to invest in the business opportunity, it was shown that it solely depends on risk perception. No theories other than risk perception predicted the decision to start a business. From the multiple regression model explaining innovative practices, it was shown that traits and positive illusions significantly added to the prediction of innovative practices. Overall findings contribute to the debate of entrepreneurship predictors and suggest that the final decision to start a business is rather determined by risk perception. The results suggest that risk perception is the factor, which may distinguish entrepreneurs from others that incline to entrepreneurship but may not found their own business and rather be innovative on the job. This study emphasizes that cognitive phenomena are applicable in explaining entrepreneurial intention and those qualities may be addressed by entrepreneurial education.
Polarization and rumpling in oxide monolayers deposited on metallic substrates

Relying on an ab initio approach to model MgO/metal interfaces, we unravel the specificity of polarization effects in the oxide monolayer limit. We show that rumpling of the supported oxide film is a structural response to the interfacial charge transfer. Surface characteristics of such complex supports can thus be directly tuned by an adequate choice of the metal and the oxide. This mechanism equally affects films of nonpolar and polar orientations. Contrary to thicker films, there is thus no electrostatic signature distinguishing the two types of orientation.
Inexact model: a framework for optimization and variational inequalities

In this paper, we propose a general algorithmic framework for the first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities (VIs). This framework allows obtaining many known methods as a special case, the list including accelerated gradient method, composite optimization methods, level-set methods, Bregman proximal methods. The idea of the framework is based on constructing an inexact model of the main problem component, i.e. objective function in optimization or operator in VIs. Besides reproducing known results, our framework allows constructing new methods, which we illustrate by constructing a universal conditional gradient method and a universal method for VIs with a composite structure. This method works for smooth and non-smooth problems with optimal complexity without a priori knowledge of the problem's smoothness. As a particular case of our general framework, we introduce relative smoothness for operators and propose an algorithm for VIs with such operators. We also generalize our framework for relatively strongly convex objectives and strongly monotone VIs.