Miracle-dz/UniFAR-FTUs huggingface dataset:
Characterization of invariant subspaces in the polydisc

We give a complete characterization of invariant subspaces for (Mz1,…,Mzn) on the Hardy space H2(Dn) over the unit polydisc Dn in Cn, n>1. In particular, this yields a complete set of unitary invariants for invariant subspaces for (Mz1,…,Mzn) on H2(Dn). As a consequence, we classify a large class of n-tuples of commuting isometries. All of our results hold for vector-valued Hardy spaces over Dn, n>1.
Coordination of a Swarm of Unicycle Robots via First-Order Dynamic Couplings

Coordination of multi-agent systems is an active and ongoing research topic. In particular, there exist several coordination strategies for multi-agent systems, in which the interaction between the agents is via static couplings, i.e. couplings that are constructed using static feedback. In contrast, this paper presents a novel coordination strategy, which introduces the use of dynamic couplings to coordinate a group of unicycle robots following a desired trajectory. The proposed control-scheme is composed by a nonlinear tracking controller and a first-order dynamic coupling. One advantage of this scheme is that, with respect to an energy index, the energy required by the dynamic coupling to perform a cooperative task is lower than the energy required by a traditional scheme based on static coupling. The stability of the closed-loop system is formally demonstrated by using the Lyapunov theory and the obtained theoretical results are illustrated with numerical simulations and validated through experiments. Also, a comparison of the proposed strategy against a coordination scheme reported in the literature, which is based on traditional static coupling, is provided. The results show that the proposed scheme has some practical implications, including reduction of the steady state error and reduced overshoot during the transient.
What's the Relation between Iron Deficiency (ID) and Febrile Seizure (FS)? A Case Control Study in Tehran, Iran

To evaluate the role of ID in the pathogenesis of FS. In this case-control study (2014-2016), 70 children were studied, 35 children with FS and 35 (controls)children with febrile diseases without convulsion (The mean age of cases was 2.191 ± 0946 vs. 1.93 ± 1.433 years in controls). Serum ferritin was estimated by the EIAS test. Data were compared between 2 groups, The ROC (receiver-operating-characteristic) curve was illustrated. The sensitivity, specificity, PPV, and NPV of the test, were calculated. Serum ferritin levels had no significant difference between the 2 groups. The ferritin level (36ng/ml) had 74.3% sensitivity, 20% specificity, 56% PPV, and 52% NPV, with a Positive likelihood Ratio being 1.3 and a Negative likelihood Ratio: 0.93 to discriminate the 2 groups. Here the ferritin level (cut-off=36ng/ml) has an acceptable sensitivity (74.3%) but poor specificity (20%) and just 56% PPV and 52% NPV to differentiate the FS cases from non-convulsive febrile children. Although a different cut-off value 21.50 ng/ml provides 91% sensitivity and very low specificity . This lower threshold cut-off might have clinically relevant outcomes in FS children if considering the other comorbidities. In our opinion, ID could not lead to FS in all children, but in some cases, with a genetic basis; ID raises the threshold for seizures. The ferritin levels as an acute phase reactant are acceptable in every febrile case. The ferritin base level in each child (case /control) before infection was unknown, but in the present study, both groups were febrile in contrast to previous studies in which ferritin levels were compared with afebrile children. Due to the high prevalence of ID (26%), especially in the young Iranian population, adding iron to the diet might help decrease FS in susceptible cases. We recommend in the future study the FS cases selected with known iron levels before convulsion.
When is a matrix unitary or Hermitian plus low rank?

Hermitian and unitary matrices are two representatives of the class of normal matrices whose full eigenvalue decomposition can be stably computed in quadratic computing complexity once the matrix has been reduced, for instance, to tridiagonal or Hessenberg form. Recently, fast and reliable eigensolvers dealing with low‐rank perturbations of unitary and Hermitian matrices have been proposed. These structured eigenvalue problems appear naturally when computing roots, via confederate linearizations, of polynomials expressed in, for example, the monomial or Chebyshev basis. Often, however, it is not known beforehand whether or not a matrix can be written as the sum of a Hermitian or unitary matrix plus a low‐rank perturbation. In this paper, we give necessary and sufficient conditions characterizing the class of Hermitian or unitary plus low‐rank matrices. The number of singular values deviating from 1 determines the rank of a perturbation to bring a matrix to unitary form. A similar condition holds for Hermitian matrices; the eigenvalues of the skew‐Hermitian part differing from 0 dictate the rank of the perturbation. We prove that these relations are linked via the Cayley transform. Then, based on these conditions, we identify the closest Hermitian or unitary plus rank k matrix to a given matrix A, in Frobenius and spectral norm, and give a formula for their distance from A. Finally, we present a practical iteration to detect the low‐rank perturbation. Numerical tests prove that this straightforward algorithm is effective.
Collaborative Service Placement, Task Scheduling, and Resource Allocation for Task Offloading With Edge-Cloud Cooperation

In an edge-cloud cooperative computing network, the task offloading performance can be further improved by the edge-cloud and edge-edge cooperation, in which the tasks can be offloaded from an edge server to the cloud server or another edge server. Such edge-cloud cooperative task offloading can jointly utilize the resources of all the edge servers and the cloud server. This paper proposes a collaborative service placement, task scheduling, computing resource allocation, and transmission rate allocation scheme for a multi-task and multi-service scenario with edge-cloud cooperation. The objective of our optimization problem is to minimize the total task processing delay while guaranteeing long-term task queuing stability. Considering the high complexity of the original optimization problem, we transform the problem into a deterministic problem for each time slot based on the Lyapunov optimization. Then, we design an iterative algorithm to obtain the whole solution to the problem efficiently based on a hybrid method using multiple numerical techniques. Further, considering the inherent difference in the optimization periods of the service placement, resource allocation, and task scheduling sub-problems, we design a multi-timescale algorithm to solve the sub-problems with different optimization periods. The complexity of the proposed algorithms is analyzed, and extensive simulations are conducted by varying multiple crucial parameters. The superiority of our scheme is demonstrated in comparison with 4 other schemes.
Stable estimation of rigid body motion using geometric mechanics

In this work, asymptotically stable state estimation schemes are proposed for rigid body motion, using the framework of geometric mechanics. Rigorous stability analyses of the estimation schemes presented here guarantee the nonlinear stability of these schemes. The stability of these schemes does not depend on the characteristics of the sensor measurement noise or external disturbances. In addition, they are robust to initial errors in the state estimates and do not need to be re-tuned when sensor noise properties change. In the first part of this dissertation, estimation of rigid body states is considered, given the dynamics model of the rigid body. In the second part, an estimation scheme that does not require knowledge of the dynamics of the rigid body is derived, based on onboard sensor measurements obtained at an appropriate frequency. The frequency of such measurements must be suitably high to resolve the motion of the rigid body. These attitude and pose estimation schemes are obtained by applying the Lagrange-d'Alembert principle from variational mechanics, to a Lagrangian constructed from state estimation errors and a dissipative term linear in the velocity estimation errors.
Using Microbenchmark Suites to Detect Application Performance Changes

Software performance changes are costly and often hard to detect pre-release. Similar to software testing frameworks, either application benchmarks or microbenchmarks can be integrated into quality assurance pipelines to detect performance changes before releasing a new application version. Unfortunately, extensive benchmarking studies usually take several hours which is problematic when examining dozens of daily code changes in detail; hence, trade-offs have to be made. Optimized microbenchmark suites, which only include a small subset of the full suite, are a potential solution for this problem, given that they still reliably detect the majority of the application performance changes such as an increased request latency. It is, however, unclear whether microbenchmarks and application benchmarks detect the same performance problems and one can be a proxy for the other. In this paper, we explore whether microbenchmark suites can detect the same application performance changes as an application benchmark. For this, we run extensive benchmark experiments with both the complete and the optimized microbenchmark suites of the two time-series database systems InfluxDB and VictoriaMetrics and compare their results to the results of corresponding application benchmarks. We do this for 70 and 110 commits, respectively. Our results show that it is possible to detect application performance changes using an optimized microbenchmark suite if frequent false-positive alarms can be tolerated.
Grid Flexibility Provision by Optimization of Fast-Charging Demand of Battery Electric Vehicles

The development of renewable energy systems and battery electric vehicles (BEVs) is essential for achieving carbon neutrality. However, the large-scale introduction of photovoltaics (PV), whose generation fluctuates, necessitates high grid flexibility. BEVs can provide flexibility by controlling the charge/discharge of batteries. This study focuses on the provision of grid flexibility by public fast-chargers. The aim of the study is to develop an optimal charging model, which considers user convenience, and estimate the provided grid flexibility by BEV fast-charging. The addition of an economic incentive to the charging rates encourages users to change their charging behavior. The charging model optimizes the charging period and amount of charge based on the charging rates. User convenience factors, such as the charging frequency and user psychology on charging, are considered. Simulations are performed using road traffic data, and the provided grid flexibility is evaluated. Three cases with different incentive rates and five groups with different user psychologies toward charging are examined. The simulation results indicate that BEV fast-charging can be used to provide grid flexibility. The fast-charging demand during the evenings and nights on weekdays, when electricity shortage is a concern, can be shifted to daytime on weekends when there is surplus electricity due to PV overgeneration.
Orbital integrals and K-theory classes

Let $G$ be a semisimple Lie group with discrete series. We use maps $K_0(C^*_rG)\to \mathbb{C}$ defined by orbital integrals to recover group theoretic information about $G$, including information contained in $K$-theory classes not associated to the discrete series. An important tool is a fixed point formula for equivariant indices obtained by the authors in an earlier paper. Applications include a tool to distinguish classes in $K_0(C^*_rG)$, the (known) injectivity of Dirac induction, versions of Selberg's principle in $K$-theory and for matrix coefficients of the discrete series, a Tannaka-type duality, and a way to extract characters of representations from $K$-theory. Finally, we obtain a continuity property near the identity element of $G$ of families of maps $K_0(C^*_rG)\to \mathbb{C}$, parametrised by semisimple elements of $G$, defined by stable orbital integrals. This implies a continuity property for $L$-packets of discrete series characters, which in turn can be used to deduce a (well-known) expression for formal degrees of discrete series representations from Harish-Chandra's character formula.
Group field theory and holographic tensor networks: dynamical corrections to the Ryu–Takayanagi formula

We introduce a generalised class of (symmetric) random tensor network states in the framework of group field theory. In this setting, we compute the Rényi entropy for a generic bipartite state via a mapping to the partition function of a topological 3D BF theory, realised as a simple interacting group field theory. The expectation value of the entanglement entropy is calculated by an expansion into stranded Feynman graphs and is shown to be captured by a Ryu–Takayanagi formula. For the simple case of a 3D BF theory, we can prove the linear corrections, given by a polynomial perturbation of the Gaussian measure, to be negligible for a broad class of networks.
Real open books and real contact structures

A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure. In this article we study open book decompositions on smooth real 3-manifolds that are compatible with the real structure. We call them real open book decompositions. We show that each real open book carries a real contact structure and two real contact structures supported by the same real open book decomposition are equivariantly isotopic. We also show that every real contact structure on a closed 3-dimensional real manifold is supported by a real open book. Finally, we conjecture that two real open books on a real contact manifold supporting the same real contact structure are related by positive real stabilizations and equivariant isotopy and that the Giroux correspondence applies to real manifolds as well namely that there is a one to one correspondence between the real contact structures on a real 3-manifold up to equivariant contact isotopy and the real open books up to positive real stabilization. Meanwhile, we study some examples of real open books and real Heegaard decompositions in lens spaces.
Effects of Therapeutic Horseback-Riding Program on Social and Communication Skills in Children with Autism Spectrum Disorder: A Systematic Review and Meta-Analysis

Animal-assisted therapy has become a fast-growing and effective approach for remediating core impairments of children with ASD; however, recent systematic review studies on the effects of AAT in children with ASD have some limitations, including referral to a variety of animal-assisted interventions rather than to horseback-riding therapy alone and the absence of any meta-analysis in systematic reviews. A complete systematic review of the studies that describe the use of THR as an intervention is needed to specifically target the core impairments of children with ASD. The purpose of this study was to employ the systematic review method to synthesize research findings regarding the effects of THR programs on the social interaction and communication skills of children with ASD. We conducted a structured search in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. We searched for potentially relevant studies in five databases (Web of Science, PubMed, CINAHL, Scopus, and SPORTDiscus) from inception until February 2022. In addition, we manually searched the bibliographies of the included studies to find articles that might otherwise have been missed. We considered articles eligible or ineligible if they satisfied specific inclusion or exclusion criteria. Our results showed that the THR program is an effective direct and alternative therapeutic program that can considerably improve the social behaviors and communication skills of children with ASD and can effectively impact autistic impairments in areas such as social awareness, social cognition, social motivation, and social communication. These findings are in line with those of previous studies; however, we did not find statistical evidence of any effect of THR on the autistic behaviors of irritability, stereotypy, and inappropriate speech. In conclusion, the findings produced by this meta-analysis study provide evidence that THR programs can considerably improve the social behaviors and communication skills of children with ASD.
The Hodge Numbers of Divisors of Calabi‐Yau Threefold Hypersurfaces

We prove a formula for the Hodge numbers of square‐free divisors of Calabi‐Yau threefold hypersurfaces in toric varieties. Euclidean branes wrapping divisors affect the vacuum structure of Calabi‐Yau compactifications of type IIB string theory, M‐theory, and F‐theory. Determining the nonperturbative couplings due to Euclidean branes on a divisor D requires counting fermion zero modes, which depend on the Hodge numbers hi(OD) . Suppose that X is a smooth Calabi‐Yau threefold hypersurface in a toric variety V, and let D be the restriction to X of a square‐free divisor of V. We give a formula for hi(OD) in terms of combinatorial data. Moreover, we construct a CW complex PD such that hi(OD)=hi(PD) . We describe an efficient algorithm that makes possible for the first time the computation of sheaf cohomology for such divisors at large h1, 1. As an illustration we compute the Hodge numbers of a class of divisors in a threefold with h1,1=491 . Our results are a step toward a systematic computation of Euclidean brane superpotentials in Calabi‐Yau hypersurfaces.
Oxidative Stability and Protective Effect of the Mixture between Helianthus annuus L. and Oenothera biennis L. Oils on 3D Tissue Models of Skin Irritation and Phototoxicity

The present study was aimed to evaluate the oxidative stability as well as to assess the protective effect of the mixture of Helianthus annuus L. (HAO) and Oenothera biennis L. (OBO) oils on 3D tissue models of skin irritation and phototoxicity. The following methods were used: GS analysis (fatty acids composition), thiobarbituric acid-reactive substances assay (TBA) (lipid oxidation degree of tested samples), 3D EpiDerm models (skin irritation and phototoxicity). For HAO the detected saturated fatty acids (SFA) were palmitic acid (7.179%), stearic acid (3.586%), eicosanoic (0.138%) and docosanoic acid (0.548%) The monounsaturated acids (MUFA) were palmitoleic acid (0.158%) and oleic acid (28.249%) and the polyunsaturated acids (PUFA) were linoleic acid (59.941%) and linolenic acid (0.208%). For OBO the detected SFA were myristic acid (0.325%), pentadecylic acid (0.281%), palmitic (7.2%), stearic (2.88%), and arachidic acid (0.275%). Regarding MUFA, even a lower proportion (8.196%) was observed, predominantly being oleic acid, cis form (7.175%), oleic (n10) (0.558%) and 11-eicosenoic (0.210%) acids. The higher content was found for PUFA (82.247%), the most significant proportions being linoleic acid (72.093%), arachidonic acid (9.812%) and linolenic (0.233%). Obtained data indicate a good oxidative stability and biocompatibility of the mixture on the 3D EpiDerm models with no irritant and no phototoxic effects. Oenothera biennis L. oil may be an excellent natural choice in order to delay or prevent oxidative damage of Helianthus annuus L. oil.
PQ-Based Local Voltage Regulation for Highly Resistive Radial Distribution Networks

Modern distributed energy resources (DER) consisting of energy storage coupled with a voltage source converter (VSC) provides flexible and dynamic operations in active and reactive power quadrants. These technologies present significant opportunities to provide distribution network support instead of traditional approaches if effective controls are in place. Although voltage regulation using reactive power is typical, active power is more effective at manipulating voltage in highly resistive distribution networks. This paper proposes a local controller that regulates VSC terminal voltage and allows fast switching of the VSC power factor output, with minimized disturbance on the terminal voltage. This improves the effectiveness of the VSC in managing voltage in highly resistive distribution networks using both active and reactive power and provides a strategy to manage upstream power flow. The approach uses gain equations derived from the voltage sensitivity to power injection and the point on wave switching in the stationary reference frame. The control strategy is verified through detailed simulation in MATLAB/Simulink using a modified IEEE 4-node test feeder, including performance during a switched load, DER disturbance and controller interaction via voltage droop. The small-signal model and stability analysis of the proposed approach is also presented.
Worst-case approximability of functions on finite groups by endomorphisms and affine maps

We study the maximum Hamming distance (or rather, the complementary notion of “minimum approximability”) of a general function on a finite group [Formula: see text] to either of the sets [Formula: see text] and [Formula: see text], of group endomorphisms of [Formula: see text] and affine maps on [Formula: see text], respectively, the latter being a certain generalization of endomorphisms. We give general bounds on these two quantities and discuss an infinite class of extremal examples (where each of the two Hamming distances can be made as large as generally possible). Finally, we compute the precise values of the two quantities for all finite groups [Formula: see text] with [Formula: see text].
Quasi-transversal in Latin Squares

In this paper, we first present the relation between a transversal in a Latin square with some concepts in its Latin square graph, and give an equivalent condition for a Latin square has an orthogonal mate. The most famous open problem involving Combinatorics is to find maximum number of disjoint transversals in a Latin square. So finding some family of decomposable Latin squares into disjoint transversals is our next aim. In the next section, we give an equivalent statement of a conjecture which has been attributed to Brualdi, Stein and Ryser by the concept of quasi-transversal. Finally, we prove the truth of the Rodney's conjecture for a family of graphs.
Eta and rho invariants on manifolds with edges

We establish existence of the eta-invariant as well as of the Atiyah-Patodi-Singer and the Cheeger-Gromov rho-invariants for a class of Dirac operators on an incomplete edge space. Our analysis applies in particular to the signature, the Gauss-Bonnet and the spin Dirac operator. We derive an analogue of the Atiyah-Patodi-Singer index theorem for incomplete edge spaces and their non-compact infinite Galois coverings with edge singular boundary. Our arguments employ microlocal analysis of the heat kernel asymptotics on incomplete edge spaces and the classical argument of Atiyah-Patodi-Singer. As an application, we discuss stability results for the two rho-invariants we have defined.