Miracle-dz/UniFAR-FTUs huggingface dataset:
Direct Search Algorithm for Numerical Solution of GARCH(1,1) Problem

Problems of estimation and forecasting of volatility are of considerable interest in various applications of economy and finance. In this paper, we propose an open program code (by C ++ language), which implements a robust heuristic algorithm for the numerical evaluation of the parameters of the linear model GARCH (1,1), with provision for its machine-dependent aspects. The program can be easily implemented by any programming language, does not require third-party mathematical procedures, so as selection of the initial values of the parameters for the model volatility. A numerical example is presented.
Stability and Robustness Analysis for a Multispecies Chemostat Model with Delays in the Growth Rates and Uncertainties

We study a chemostat model with an arbitrary number of competing species, one substrate, and constant dilution rates. We allow delays in the growth rates and additive uncertainties. Using constant inputs of certain species, we derive bounds on the sizes of the delays that ensure asymptotic stability of an equilibrium when the uncertainties are zero, which can allow persistence of multiple species. Under delays and uncertainties, we provide bounds on the delays and on the uncertainties that ensure input-to-state stability with respect to uncertainties.
Full scattering profile for detecting physiological tissue properties

Light reflectance and transmission from soft tissue has been utilized in noninvasive clinical measurement devices such as the photoplethysmograph (PPG) and reflectance pulse oximeter. Most methods of near infrared (NIR) spectroscopy focus on the volume reflectance from a semi-infinite sample, while very few measure transmission. We have previously shown that examining the full scattering profile (FSP), which is the angular distribution of exiting photons, provides more comprehensive information when measuring from a cylindrical tissue, such as earlobe, fingertip and pinched tissue. Our hypothesis is that the change in blood vessel diameter is more significant than the change in optical properties. The findings of this work demonstrate a realistic model for optical tissue measurements such as NIR spectroscopy, PPG and pulse oximetery.
The Weakly Nilpotent Graph of a Commutative Ring

Abstract Let $R$ be a commutative ring with non-zero identity. In this paper, we introduce the weakly nilpotent graph of a commutative ring. The weakly nilpotent graph of $R$ denoted by ${{\Gamma }_{w}}(R)$ is a graph with the vertex set ${{R}^{\star }}$ and two vertices $x$ and $y$ are adjacent if and only if $x\,y\in N{{(R)}^{\star }}$ , where ${{R}^{\star }}=R\backslash \{0\}$ and $N{{(R)}^{\star }}$ is the set of all non-zero nilpotent elements of $R$ . In this article, we determine the diameter of weakly nilpotent graph of an Artinian ring. We prove that if ${{\Gamma }_{w}}(R)$ is a forest, then ${{\Gamma }_{w}}(R)$ is a union of a star and some isolated vertices. We study the clique number, the chromatic number, and the independence number of ${{\Gamma }_{w}}(R)$ . Among other results, we show that for an Artinian ring $R$ , ${{\Gamma }_{w}}(R)$ is not a disjoint union of cycles or a unicyclic graph. For Artinan rings, we determine diam $\overline{({{\Gamma }_{w}}(R))}$ . Finally, we characterize all commutative rings $R$ for which $\overline{({{\Gamma }_{w}}(R))}$ is a cycle, where $\overline{({{\Gamma }_{w}}(R))}$ is the complement of the weakly nilpotent graph of $R$ .
Model selection in block clustering by the integrated classification likelihood

Block clustering (or co-clustering) aims at simultaneously partitioning the rows and columns of a data table to reveal homogeneous block structures. This structure can stem from the latent block model which provides a probabilistic modeling of data tables whose block pattern is defined from the row and column classes. For continuous data, each table entry is typically assumed to follow a Gaussian distribution. For a given data table, several candidate models are usually examined: they may differ in the numbers of clusters or in the number of free parameters. Model selection then becomes a critical issue, for which the tools that have been derived for model-based one-way clustering need to be adapted. In one-way clustering, most selection criteria are based on asymptotical considerations that are difficult to render in block clustering due to dual nature of rows and columns. We circumvent this problem by developing a non-asymptotic criterion based on the Integrated Classification Likelihood. This criterion can be computed in closed form once a proper prior distribution has been defined on the parameters. The experimental results show steady performances for medium to large data tables with well-separated and moderately-separated clusters.
Semi‐global cooperative output regulation of a class of nonlinear uncertain multi‐agent systems under switching networks

In this paper, we consider the semi‐global cooperative output regulation problem for a class of nonlinear uncertain multi‐agent systems under switching networks. At first, we study the nonadaptive case when the exosystem has no parametric uncertainties and construct a common Lyapunov function to achieve the output regulation for general switching connected networks. Next, we study the case when the exosystem contains some parametric uncertainties. To solve the problem, we establish a stability result for a class of time‐varying system, which is then used in the design of distributed adaptive internal model‐based control. Then we construct multiple Lyapunov functions for the switching signal with its average dwell time lower bounded by a given constant. Throughout the paper, we treat the closed‐loop multi‐agent system from the viewpoint of singular perturbation. In fact, the singular perturbation‐based method provides an effective tool to handle the multi‐agent system under switching networks. Finally, we give numerical simulations based on Duffing systems and flexible manipulator systems to illustrate the effectiveness of our method. Copyright © 2017 John Wiley & Sons, Ltd.
Twin-subset semantic model for intention

Intention, an indispensable cognition attribute of agent, plays an important role in agent's rational behavior. There is a lot of research on formalization of cognitive state that include intentions of the agents in a multi-agent system. These theories are based on normal modal logic, interpret intention as unary normal modal operator in Kripke semantics, and hence suffer from the harmful logical omniscience and side-effect problems. These have not been eliminated satisfactorily as yet. In this paper, we interpret intention as unary non-normal modal operator and introduce novel possible world semantics for intention, called the twin-subset semantics. It describes the intentions of agent in a possible world w with two subsets of W, where W is the set of all possible worlds which an agent can be in, and allows us to embody essential cognitive features of intention and the relations between belief and intention. Compared with classical normal or non-normal modal logics, not only does it avoid the logical omniscience and side-effect problems but also the classical semantics of logical connectives are still valid; and moreover, it improves the true-false subset semantics, which were introduced by us previously, and overcomes its serious drawbacks.
Affine registration of three-dimensional point sets for improving the accuracy of eye position trackers

Abstract. Existing methods for tracking three-dimensional (3-D) eye positions with a monocular color camera mostly rely on a generic 3-D face model and a certain face database. However, the performance of these methods is susceptible to the variations of head poses. For this reason, existing methods for estimating 3-D eye position from a single two-dimensional face image may yield erroneous results. To improve the accuracy of 3-D eye position trackers using a monocular camera, we present a compensation method as a postprocessing technique. We address the problem of determining an optimal registration function for fitting 3-D data consisting of the inaccurate estimates from the eye position tracker and their corresponding ground truths. To obtain the ground truths of 3-D eye positions, we propose two different systems by combining an optical motion capture system and checkerboards, which construct the form of the hand-eye and robot-world calibration. By solving a least-squares optimization problem, we can determine the optimal registration function in an affine form. Real experiments demonstrate that the proposed method can considerably improve the accuracy of 3-D eye position trackers using a single color camera.
Machine-learning prediction of fluid variables from data using reservoir computing

We predict both microscopic and macroscopic variables of a chaotic fluid flow using reservoir computing. In our procedure of the prediction, we assume no prior knowledge of physical model describing a fluid flow except that its behavior is complex but deterministic. We present two ways of prediction of the complex behavior; the first called partial-prediction requires continued knowledge of partial time-series data during the prediction as well as past time-series data, while the second called full-prediction requires only past time-series data as training data. For the first case, we are able to predict long-time motion of microscopic fluid variables. For the second case, we show that the reservoir dynamics constructed from only past data of energy functions can predict the future behavior of energy functions and reproduce the energy spectrum. This implies that the obtained reservoir system constructed without the knowledge of microscopic data is equivalent to the dynamical system describing macroscopic behavior of energy functions.
Geometric Relationship between Stereo Disparity and Optical Flow and an Efficient Recursive Algorithm

We suggest a relationship, called stereo-motion equation, between stereo disparity and optical flow, and a recursive filter, as an efficient algorithm to estimate the two quantities. We show that close spatial and temporal relationships exist between the two quantities. The importance of this discovery is that the vision quantities can be computed simultaneously, on the image level, unlike previous approaches that tried to determine the two quantities separately. This algorith m is general because it can be reduced to the separate methods to estimate either disparity or optical flow. Because the two vision quantities help mutually for the best matches, the results tend to be more accurate and reliable than the separate methods. As an efficient algorithm, we suggest a recursive filter in which the two vis ion quantities are determined alternatively by time and measurement updates. This algorithm was tested on both synthetic and natural scenes containing moving objects and performed better than separate calculation of disparity and optical flow.
Maximizing Transmission Rates for Pairwise Multiway Relay Channel

In this dissertation, we study the e↵ect of users’ transmission ordering on the common rate and sum rate of pairwise multiway relay channels (MWRCs). As an extension for two-way relay channel (TWRC), MWRC has been proposed to improve the spectral e ciency in wireless networks. In a pairwise scheme, a set of pairs, known as ordering, is defined that represents the users’ transmission schedule. Each pair of users form a TWRC and simultaneously send their data to the relay in an uplink phase. There are di↵erent strategies for the relay to form the downlink message. We consider decode-and-forward and functional-decode-forward relaying strategies for our study. We find the ordering that achieves the maximum e ciency of the pairwise MWRC. To find transmission orderings that maximize the common rate and sum rate of the system, we first develop a graphical model for the data transmission in a pairwise MWRC. Using the proposed graphical model, we, then, find the necessary and su cient conditions for an ordering to be feasible (i.e., allows for successful decoding). Using this model, we finally find the optimal orderings that achieve the maximum common rate and sum rate of the system, respectively. Closed form expressions for the maximum achievable common rate and sum rate are also found. Computer simulations are presented for better illustration and comparison between the rate metrics of the proposed optimal orderings and random orderings. ii
Pathwise construction of certain moment dualities and application to population models with balancing selection

We investigate dual mechanisms for interacting particle systems. Generalizing an approach of Alkemper and Hutzenthaler in the case of coalescing duals, we show that a simple linear transformation leads to a moment duality of suitably rescaled processes. More precisely, we show how dualities of interacting particle systems of the form $H(A,B)=q^{|A\cap B|}, A,B\subset\{0,1\}^N, q\in[-1,1),$ are rescaled to yield moment dualities of rescaled processes. We discuss in particular the case $q=-1,$ which explains why certain population models with balancing selection have an annihilating dual process. We also consider different values of $q,$ and answer a question by Alkemper and Hutzenthaler.
Theories of central engine for long gamma-ray bursts

Long GRBs are the most powerful explosions in the universe since the Big Bang. At least, some fraction of long GRBs are born from the death of massive stars. Likewise, only some fraction of massive stars that satisfy additional special conditions explode as long GRBs associated with supernovae/hypernovae. In this paper, we discuss the explosion mechanism of long GRBs associated with hypernovae: ‘the central engine of long GRBs’. The central engine of long GRBs is very different from that of core-collapse supernovae, although the mechanism of the engine is still not firmly established. In this paper, we review theoretical studies of the central engine of long GRBs. First, we discuss possible progenitor stars. Then several promising mechanisms of the central engine—such as black hole and magnetar formation—will be reviewed. We will also mention some more exotic models. Finally, we describe prospects for future studies of the central engine of long GRBs.
Radiologische Rekanalisation von Venen, Gefäßprothesen und Arterien bei insuffizienten Dialysefisteln

stenoses and one occlusion - proved successful. In 19 patients with oederna of the arm. 30 dilatations of central veins were perforrned (18 stenoses, one occlusion). The recanalisation rate was 97% (29/30), the six months patency rate was 57% (8/14). The long-term results of radiological recanalisation are comparable with surgical revision by patcli plasty or thrombectomy, but the radiological techiiiques are simpler, can be carried out on out patients and can be repeated if necessary.
Inference for Errors-in-Variables Models in the Presence of Systematic Errors with an Application to a Satellite Remote Sensing Campaign

ABSTRACT Motivated by a satellite remote sensing mission, this article proposes a multivariable errors-in-variables (EIV) regression model with heteroscedastic errors for relating the satellite data products to similar products from a well-characterized but globally sparse ground-based dataset. In the remote sensing setting, the regression model is used to estimate the global divisor for the satellite data. The error structure of the proposed EIV model comprises two components: A random-error component whose variance is inversely proportional to sample size of underlying individual observations which are aggregated to obtain the regression data, and a systematic-error component whose variance remains the same as the underlying sample size increases. In this article, we discuss parameter identifiability for the proposed model and obtain estimates from two-stage parameter estimation. We illustrate our proposed procedure through both simulation studies and an application to validating measurements of atmospheric column-averaged CO2 from NASA’s Orbiting Carbon Observatory-2 (OCO-2) satellite. The validation uses coincident target-mode OCO-2 data that are temporally and spatially sparse and ground-based measurements from the Total Carbon Column Observing Network (TCCON) that are spatially sparse but more accurate. Supplementary materials for the article are available online.
The spin-valve transistor

High density magnetic recording, magnetic random access memories, displacement and current detection, contactless switching and electronic compass applications all require magnetic field sensors with unprecedented sensitivity. The spin-valve effect (giant magnetoresistance) found in 1988 in magnetic metallic multilayers provided a new form of magnetoresistance with promising possibilities. The name indicates its physical origin: the magnetic layers form magnetic field controllable valves for electrons with parallel spins, leading to low resistance under application of a magnetic field. The resistance is usually measured using a four point technique, with the current in plane. Now, ten years later, the first hard disk incorporating this effect has reached the marketplace. Its read head shows a spin-valve effect of about 5% allowing for a capacity of 16.8 Gbyte. The use of the much larger perpendicular spin-valve effect was limited because of the ultra low perpendicular resistance of the atomically thin multilayers. Subject of this thesis is the spin valve transistor, which we introduced 1995. It is able to circumvent the low resistance dilemma by its direct mean free path dependence in the output. In the spin valve transistor a spin-valve multilayer serves as a base region of an n-silicon metal base transistor structure: via an emitter barrier hot electrons are injected into the spin-valve, a collector barrier accepts only non-scattered electrons by means of its angle and energy selectivity. Since the number of collected electrons depends exponentially on the spin dependent mean free path in the spin-valve base, and since the mean free path changes with field due to the perpendicular spin-valve effect, the collector current change with magnetic field is much larger than the resistance change in current-in-plane measurements and can be effectively used for magnetic field detection. Since the electron energy of the injected electrons can be varied either using different Schottky barriers or bias variation using a tunnel emitter, the spin-valve transistor allows electron spectroscopy to be performed in spin-valves. Because the electron energy range is of the same order as the spin-split 3d bands of the ferromagnetic metals Co, Fe and Ni, a direct investigation of the spin-dependent band structure which causes the spin-valve effect is possible. An extension of the two channel model has been formulated, showing that the collector current change can be extremely large, for example, implementation of a 5% spin-valve (measured in plane) may lead to practically useful output current variations of more than 500%. Moreover, thickness variation e.g. using wedges, allows determination of spin dependent mean free paths.
APPROXIMATION WITH GENERALIZED HYPEREXPONENTIAL DISTRIBUTIONS: WEAK CONVERGENCE RESULTS*

Generalized hyperexponential (GH) distributions are linear combinations of exponential CDFs with mixing parameters (positive and negative) that sum to unity. The denseness of the class GH with respect to the class of all CDFs deemed on [0, **) is established by showing that a GH distr~ution can be found that is as close to a given CDF as desired, with respect to a suitably defined metric. The metric induces the usual topology of weak convergence so that, equivalently, there exists a sequence of GH CDFs that converges weakly to a given CDF. This result is established by using a similar result for weak convergence of Edang mixtures. Various set inclusion relations are also obtained relating the GH distributions to other commonly used classes of approximating distributions, including generalized Erlang (GE), mixed generalized Eflang (MGE), those with reciprocal polynomial Laplace transforms (Kn), those with rational Laplace transforms (Rn), and phasetype (PH) distributions. A brief survey of the history and use of approximating distributions in queueing theory is also included.
Characterizations of Right Weakly Regular Semigroups in Terms of Generalized Cubic Soft Sets

Cubic sets are the very useful generalization of fuzzy sets where one is allowed to extend the output through a subinterval of [ 0 , 1 ] and a number from [ 0 , 1 ] . Generalized cubic sets generalized the cubic sets with the help of cubic point. On the other hand Soft sets were proved to be very effective tool for handling imprecision. Semigroups are the associative structures have many applications in the theory of Automata. In this paper we blend the idea of cubic sets, generalized cubic sets and semigroups with the soft sets in order to develop a generalized approach namely generalized cubic soft sets in semigroups. As the ideal theory play a fundamental role in algebraic structures through this we can make a quotient structures. So we apply the idea of neutrosophic cubic soft sets in a very particular class of semigroups namely weakly regular semigroups and characterize it through different types of ideals. By using generalized cubic soft sets we define different types of generalized cubic soft ideals in semigroups through three different ways. We discuss a relationship between the generalized cubic soft ideals and characteristic functions and cubic level sets after providing some basic operations. We discuss two different lattice structures in semigroups and show that in the case when a semigroup is regular both structures coincides with each other. We characterize right weakly regular semigroups using different types of generalized cubic soft ideals. In this characterization we use some classical results as without them we cannot prove the inter relationship between a weakly regular semigroups and generalized cubic soft ideals. This generalization leads us to a new research direction in algebraic structures and in decision making theory.
AN OTHER PROOF OF THE INSOLUBILITY OF FERMAT'S CUBIC EQUATION IN EISENSTEIN'S RING

We present an other proof of the well known insolubility of Fermat’s equation x3 + y3 = z3 in Eisenstein’s ring Z[ω] when ω3 = 1, ω ̸= 1, x y z ̸= 0. Assuming the existence of a nontrivial solution (a1 + b1 ω, a2 + b2 ω, a3 + b3 ω) the proof exploits the algebraic properties, (degree, kind of roots, coefficients’ relations), of the polynomial f(x) = (a1 + b1 x)3 + (a2 + b2 x)3 − (a3 + b3 x)3. In the course of action, the well known algebraic structure of the group of rational points of the elliptic curve y2 = x3 + 16 provides the final result.