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Effectively designing molecular geometries is essential to advancing pharmaceutical innovations, a domain, which has experienced great attention through the success of generative models and, in particular, diffusion models. However, current molecular diffusion models are tailored towards a specific downstream task and lack adaptability. We introduce UniGuide, a framework for controlled geometric guidance of unconditional diffusion models that allows flexible conditioning during inference without the requirement of extra training or networks. We show how applications such as structure-based, fragment-based, and ligand-based drug design are formulated in the UniGuide framework and demonstrate on-par or superior performance compared to specialised models. Offering a more versatile approach, UniGuide has the potential to streamline the development of molecular generative models, allowing them to be readily used in diverse application scenarios., Comment: 38th Conference on Neural Information Processing Systems (NeurIPS)

This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a fixed point algorithm and a Riemannian optimization method based on the derived information geometry of Elliptical Wishart distributions. The existence and uniqueness of the MLE are characterized as well as the convergence of both estimation algorithms. Statistical properties of the MLE are also investigated such as consistency, asymptotic normality and an intrinsic version of Fisher efficiency. On the statistical learning side, novel classification and clustering methods are designed. For the $t$-Wishart distribution, the performance of the MLE and statistical learning algorithms are evaluated on both simulated and real EEG and hyperspectral data, showcasing the interest of our proposed methods.

In this paper we consider the discrete Laplacian acting on 1-forms and we study its spectrum relative to the spectrum of the 0-form Laplacian. We show that the non zero spectrum can coincide for these Laplacians with the same nature. We examine the characteristics of 0-spectrum of the 1-form Laplacian compared to the cycles of graphs.

This paper deals with the Elliptical Wishart and Inverse Elliptical Wishart distributions, which play a major role when handling covariance matrices. Similarly to multivariate elliptical distributions, these form a large family of covariance distributions, encompassing, e.g., the Wishart or \textit{t}-Wishart ones. Our first major contribution is to derive a stochastic representation for Elliptical Wishart and Inverse Elliptical Wishart matrices. This later enables us to obtain various key statistical properties of Elliptical Wishart and Inverse Elliptical Wishart distributions such as expectations, variances, and Kronecker moments up to any orders. The stochastic representation also allows us to provide an efficient method to generate random matrices from Elliptical Wishart and Inverse Elliptical Wishart distributions. Finally, the practical interest of Elliptical Wishart distributions - in particular the \textit{t}-Wishart one - is demonstrated through a fitting experiment on real electroencephalographic data. This showcases their effectiveness in accurately modeling real covariance matrices.

This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure to match the double twisted bialgebra axioms is explicitly described.

The finite topological quandles can be represented as $n\times n$ matrices, recently defined by S. Nelson and C. Wong. In this paper, we first study the finite topological quandles and we show how to use these matrices to distinguish all isomorphism classes of finite topological quandles for a given cardinality $n$. As an application, we classify finite topological quandles with up to 4 elements.

This paper proposes a method for automatically monitoring and analyzing the evolution of complex geographic objects. The objects are modeled as a spatiotemporal graph, which separates filiation relations, spatial relations, and spatiotemporal relations, and is analyzed by detecting frequent sub-graphs using constraint satisfaction problems (CSP). The process is divided into four steps: first, the identification of complex objects in each satellite image; second, the construction of a spatiotemporal graph to model the spatiotemporal changes of the complex objects; third, the creation of sub-graphs to be detected in the base spatiotemporal graph; and fourth, the analysis of the spatiotemporal graph by detecting the sub-graphs and solving a constraint network to determine relevant sub-graphs. The final step is further broken down into two sub-steps: (i) the modeling of the constraint network with defined variables and constraints, and (ii) the solving of the constraint network to find relevant sub-graphs in the spatiotemporal graph. Experiments were conducted using real-world satellite images representing several cities in Saudi Arabia, and the results demonstrate the effectiveness of the proposed approach.

The segmentation and automatic identification of histological regions of diagnostic interest offer a valuable aid to pathologists. However, segmentation methods are hampered by the difficulty of obtaining pixel-level annotations, which are tedious and expensive to obtain for Whole-Slide images (WSI). To remedy this, weakly supervised methods have been developed to exploit the annotations directly available at the image level. However, to our knowledge, none of these techniques is adapted to deal with WSIs. In this paper, we propose WholeSIGHT, a weakly-supervised method, to simultaneously segment and classify WSIs of arbitrary shapes and sizes. Formally, WholeSIGHT first constructs a tissue-graph representation of the WSI, where the nodes and edges depict tissue regions and their interactions, respectively. During training, a graph classification head classifies the WSI and produces node-level pseudo labels via post-hoc feature attribution. These pseudo labels are then used to train a node classification head for WSI segmentation. During testing, both heads simultaneously render class prediction and segmentation for an input WSI. We evaluated WholeSIGHT on three public prostate cancer WSI datasets. Our method achieved state-of-the-art weakly-supervised segmentation performance on all datasets while resulting in better or comparable classification with respect to state-of-the-art weakly-supervised WSI classification methods. Additionally, we quantify the generalization capability of our method in terms of segmentation and classification performance, uncertainty estimation, and model calibration.

Spatial data structures allow to make efficient queries on Geographical Information Systems (GIS). Spatial queries involve the geometry of the data, such as points, lines, or polygons. For instance, a spatial query could poll for the nearest restaurants from a given location. Spatial queries can be solved exhaustively by going through the entire data, which is prohibitive as the number of data points increases. In this article, we are interested in making efficient queries on infinitely long geometrical shapes. For instance, angular sectors, defined as the intersection of two half-spaces, are infinitely long. However, regular spatial data structures are not adapted to these geometrical shapes. We propose a new method allowing to make efficient spatial queries on angular sectors (i.e. whether a point is inside an angular sector). It builds a R-tree from the dual space of angular sectors. An extensive evaluation shows our method is faster than using a regular R-tree., Comment: 18 pages

In this paper, we first recall the construction of a twisted pre-Lie algebra structure on the species of finite connected topological spaces. Then we construct the corresponding nonassociative permutative coproduct, and we prove that the vector space generated by isomorphism classes of finite posets is a free pre-Lie algebra and is a co-free non-associative permutative coalgebra. In the end, we give an explicit duality between the non-associative permutative product and the proposed non-associative permutative coproduct. Finally, we prove that the results in this paper remain true for the finite connected topological spaces.

Superconducting quantum computing is experiencing a tremendous growth. Although major milestones have already been achieved, useful quantum-computing applications are hindered by a variety of decoherence phenomena. Decoherence due to two-level systems (TLSs) hosted by amorphous dielectric materials is ubiquitous in planar superconducting devices. We use high-quality quasilumped element resonators as quantum sensors to investigate TLS-induced loss and noise. We perform two-tone experiments with a probe and pump electric field; the pump is applied at different power levels and detunings. We measure and analyze time series of the quality factor and resonance frequency for very long time periods, up to 1000 h. We additionally carry out simulations based on the TLS interacting model in presence of a pump field. We find that loss and noise are reduced at medium and high power, matching the simulations, but not at low power., Comment: 20 two-column pages (including App. and Supplement), 12 figures, 3 tables

Constraint satisfaction problem (CSP) has been actively used for modeling and solving a wide range of complex real-world problems. However, it has been proven that developing efficient methods for solving CSP, especially for large problems, is very difficult and challenging. Existing complete methods for problem-solving are in most cases unsuitable. Therefore, proposing hybrid CSP-based methods for problem-solving has been of increasing interest in the last decades. This paper aims at proposing a novel approach that combines incomplete and complete CSP methods for problem-solving. The proposed approach takes advantage of the group search algorithm (GSO) and the constraint propagation (CP) methods to solve problems related to the remote sensing field. To the best of our knowledge, this paper represents the first study that proposes a hybridization between an improved version of GSO and CP in the resolution of complex constraint-based problems. Experiments have been conducted for the resolution of object recognition problems in satellite images. Results show good performances in terms of convergence and running time of the proposed CSP-based method compared to existing state-of-the-art methods.

The notions of magnetic difference operator defined on weighted graphs or magnetic exterior derivative are discrete analogues of the notionof covariant derivative on sections of a fibre bundle and its extension on differential forms. In this paper, we extend this notion to certain 2-simplicial complexes called triangulations, in a manner compatible with changes of gauge. Then we study the magnetic Gauss-Bonnet operator naturally defined in this context and introduce the geometric hypothesis of $\chi-$completeness which ensures the essential self-adjointness of this operator. This gives also the essential self-adjointness of the magnetic Laplacian on triangulations. Finally we introduce an hypothesis of bounded curvature for the magnetic potential which permits to characterize the domain of the self-adjoint extension., Comment: {\`a} para{\^i}tre dans Filomat

In this paper, we first study the species of finite topological spaces recently considered by F. Fauvet, L. Foissy, and D. Manchon. Then, we construct a twisted pre-Lie structure on the species of connected finite topological spaces. The underlying pre-Lie structure defines a coproduct on the species of finite topological spaces different from those already defined by the Authors above. In the end, we illustrate the link between the Grossman-Larson product and the proposed coproduct.

Cattle activity is an essential index for monitoring health and welfare of the ruminants. Thus, changes in the livestock behavior are a critical indicator for early detection and prevention of several diseases. Rumination behavior is a significant variable for tracking the development and yield of animal husbandry. Therefore, various monitoring methods and measurement equipment have been used to assess cattle behavior. However, these modern attached devices are invasive, stressful and uncomfortable for the cattle and can influence negatively the welfare and diurnal behavior of the animal. Multiple research efforts addressed the problem of rumination detection by adopting new methods by relying on visual features. However, they only use few postures of the dairy cow to recognize the rumination or feeding behavior. In this study, we introduce an innovative monitoring method using Convolution Neural Network (CNN)-based deep learning models. The classification process is conducted under two main labels: ruminating and other, using all cow postures captured by the monitoring camera. Our proposed system is simple and easy-to-use which is able to capture long-term dynamics using a compacted representation of a video in a single 2D image. This method proved efficiency in recognizing the rumination behavior with 95%, 98% and 98% of average accuracy, recall and precision, respectively., Comment: 17 pages, 6 figures, 4 tables

The species of finite topological spaces admits two graded bimonoid structures, recently defined by F. Fauvet, L. Foissy, and the second author. In this article, we define a doubling of this species in two different ways. We build a bimonoid structure on each of these species and describe a cointeraction between them. We also investigate two related associative products obtained by dualisation., Comment: Version 3. Extended introduction and bibliography

While Roth's theorem states that the irrationality measure of all the irrational algebraic numbers is 2, and the same holds true over function fields in characteristic zero, some counter-examples were found over function fields in positive characteristic. This was put forward first by Mahler in 1949, in his fundamental paper on Diophantine approximation \cite{M}. It seems that, except for particular elements, as power series with bounded partial quotients, Roth's theorem holds. Until now, only one element, with unbounded partial quotients, discovered by Mills and Robbins \cite{MR} in 1986, has been recognized having this property. It concerns a quartic power series over $\mathbb{F}_{3}$ having a continued fraction expansion with remarkable pattern. This continued fraction expansion was explicitly described by Buck and Robbins \cite{BR}, and later by Lasjaunias \cite{LA2} who used another method somewhat easier. Furthermore, Lasjaunias \cite{LA2} improve the value of its irrationality measure in relation with Roth's theorem. We will see that this power series is included in a large quartic power series family, for which the continued fraction expansion and the irrationality measure can be explicitly given. Moreover, we will study the rational approximation of other examples of quartic power series over $\mathbb{F}_{3}$ and we will extend the set of counter-examples initiated by Mahler., Comment: 24 pages

The minimization of the loss function is of paramount importance in deep neural networks. On the other hand, many popular optimization algorithms have been shown to correspond to some evolution equation of gradient flow type. Inspired by the numerical schemes used for general evolution equations we introduce a second order stochastic Runge Kutta method and show that it yields a consistent procedure for the minimization of the loss function. In addition it can be coupled, in an adaptive framework, with a Stochastic Gradient Descent (SGD) to adjust automatically the learning rate of the SGD, without the need of any additional information on the Hessian of the loss functional. The adaptive SGD, called SGD-G2, is successfully tested on standard datasets.

Classical voting rules assume that ballots are complete preference orders over candidates. However, when the number of candidates is large enough, it is too costly to ask the voters to rank all candidates. We suggest to fix a rank k, to ask all voters to specify their best k candidates, and then to consider "top-k approximations" of rules, which take only into account the top-k candidates of each ballot. We consider two measures of the quality of the approximation: the probability of selecting the same winner as the original rule, and the score ratio. We do a worst-case study (for the latter measure only), and for both measures, an average-case study and a study from real data sets., Comment: 17 pages, 7 figures

We study quadratic approximations for two families of hyperquadratic continued fractions in the field of Laurent series over a finite field. As the first application, we give the answer to a question of the second author concerning Diophantine exponents for algebraic Laurent series. As the second application, we determine the degrees of these families in particular case., Comment: 11 pages

In this paper, we are concerned with the state feedback stabilization of ODE-PDE cascade systems governed by a linear ordinary differential equation and the 1-d reaction-diffusion equation posed on a bounded interval. In contrast to the previous works in the literature where the control acts at the boundary, the control for the entire system acts at an inside point of the PDE domain whereas the PDE acts in the linear ODE by a Neumann connection. We use the infinite dimensional backstepping design to convert system under consideration to an exponentially target system. By invertibility of the design and Lyapunov analysis, we prove the well posedness and exponential stability of such system.

In this paper, we solve the problem of exponential stabilization for a class of cascade ODE-PDE system governed by a linear ordinary differential equation and a 1-d linearized Korteweg-de Vries equation (KdV) posed on a bounded interval. The control for the entire system acts on the left boundary with Dirichlet condition of the KdV equation whereas the KdV acts in the linear ODE by a Dirichlet connection. We use the socalled backstepping design in infinite dimension to convert the system under consideration into an exponentially stable cascade ODE-PDE system.Then, we use the invertibility of such design to achieve the exponential stability for the ODE-PDE cascade system under consideration by using Lyapunov analysis.

In the context of an infinite locally finite weighted graph, we give a necessary and sufficientcondition for semi-Fredholmness of the Gauss-Bonnet operator. This result is a discrete version of thetheorem of Gilles Carron in the continuous case [5]. In addition, using a criterion of Anghel [2], we givea sufficient condition to have an operator of Gauss-Bonnet with closed range. Finally, this work can beconsidered as an extension of the work of Colette Ann\'e and Nabila Torki-Hamza [3]., Comment: mon article est accept\'e pour publication dans Filomat

Conventional OFDM, adopted in LTE-A systems, cannot provide the quality of service requirements sought in 5G systems because of extreme natural channel impairments caused by higher Doppler spreads and unexpected artificial impairments caused by multi-source transmission, to be brought by 5G, and by synchronization relaxation for closed-loop signaling overhead reduction in some 5G applications. These severe impairments induce a strong loss of orthogonality between subcarriers and OFDM symbols and, therefore, lead to a dramatic increase in ICI and ISI. To be well armed against these dramatic impairments, we, in the present paper, optimize the transmit/receive waveforms for FBMC systems, with hexagonal time-frequency lattices, operating over severe doubly dispersive channels, accounting for both natural and artificial impairments. For this, we exploit the POPS paradigm, recently proposed for rectangular time-frequency lattices, to design offline waveforms maximizing the SINR for hexagonal time-frequency lattices. We show that FBMC, with hexagonal lattices, offers a strong improvement in SIR with respect to conventional OFDM and an improvement of 1dB with respect to POPS-FBMC, with classical rectangular lattices. Furthermore, we show that the hexagonal POPS-FBMC brings more robustness to frequency synchronization errors and offers a 10dB reduction in OOB emissions with respect to rectangular POPS-FBMC.

We present both full quantum mechanical and semiclassical calculations of above threshold ionization (ATI) of a hydrogen atom in the tunneling regime by a few-cycle linearly polarized infrared laser pulse. As a quantum treatment, we applied the direct integration of the time dependent Schr\"odinger equation (TDSE). In the semiclassical approximation (SCA), it is assumed that wavepacket propagation in the post-tunneling process can be well described within the classical framework. With these two methods, we analyze the similarities and deviations for ionization of the hydrogen atom. We found that the 3 dimensional semiclassical method can describe reasonably well the momentum correlation pattern of the ATI peaks. We also show good agreement between the results obtained by TDSE method and the semi-classical method. Furthermore, with the semiclassical approximation we clearly identify and separate the regions in momentum distributions of the ejected electrons according to initial conditions. We illustrate the corresponding regions with typical electron trajectories., Comment: 7 pages, 6 figures

The interaction of a short, few-cycle light pulse and an atom which is prepared initially in a superposition of two stationary states is shown to exhibit strong signatures of atomic coherence. For a given waveform of the laser pulse, appropriate quantum mechanical relative phase between the constituents of the initial superposition can increase the ionization probability by a factor of three. A similarly strong effect can be observed when the waveform of the ionizing pulse is changed. These results allow for intuitive explanations, which are in agreement with the numerical integration of the time dependent Schr\"{o}dinger equation., Comment: 11 pages, 6 figures

In this work, we consider a nonlinear vibrating Timoshenko system with thermoelasticity with second sound. We recall first the results of well-posdness and regularity and the asymptotic behavior of the energy obtained in \cite{Ayadi}. Then, we use a fourth order finite difference scheme to compute the numerical solutions and thus we show the energy decay in several cases depending on the stability number. R\'esum\'e : Dans ce travail, on consid\`ere le syst\`eme de Timoshenko non-lin\'eaire avec Thermo-\'elasticit\'e et deuxi\`eme son. On rappelle d'abord les r\'esultats d'existence, de r\'egularit\'e et du comportement asymptotique de l'\'energie obtenus dans \cite{Ayadi}. Ensuite, on valide num\'eriquement ces r\'esultats th\'eoriques. Pour cela, on utilise une m\'ethode de diff\'erences finies d'ordre $4$. Ainsi la solution num\'erique obtenue permet de valider la d\'ecroissance de l'\'energie dans plusieurs cas selon la valeur du param\`etre de stabilit\'e., Comment: 10 pages

In this article, we consider a vibrating nonlinear Timoshenko system with thermoelasticity with second sound. We discuss the well-posedness and the regularity of Timoshenko solution using the semi-group theory. Moreover, we etablish an explicit and general decay results for a wide class of relaxating functions which depend on a stability number $\mu$., Comment: 25 pages

Given a compact Riemannian manifold, we prove a uniform Franks' lemma at second order for geodesic flows and apply the result in persistence theory., Comment: 60 pages

Casually introduced thirty years ago, a simple algebraic equation of degree 4, with coefficients in Fp[T], has a solution in the field of power series in 1/T, over the finite field Fp. For each prime p > 3, the continued fraction expansion of this solution is remarkable and it has a different general pattern according to the remainder, 1 or 2, in the division of p by 3. We describe two very large families of algebraic continued fractions, each containing these solutions, according to the class of p modulo 3. We can compute the irrationality measure for these algebraic continued fractions and, as a consequence, we obtain two different values for the solution of the quartic equation, only depending on the class of p modulo 3., Comment: 21 pages, 2 figures

We provide an elementary proof of the Franks lemma for geodesic flows that uses basic tools of geometric control theory., Comment: 14 pages, 2 figures

Motivated by the increased need for formalized representations of the domain of Data Mining, the success of using Formal Concept Analysis (FCA) and Ontology in several Computer Science fields, we present in this paper a new approach for automatic generation of Fuzzy Ontology of Data Mining (FODM), through the fusion of conceptual clustering, fuzzy logic, and FCA. In our approach, we propose to generate ontology taking in consideration another degree of granularity into the process of generation. Indeed, we suggest to define an ontology between classes resulting from a preliminary classification on the data. We prove that this approach optimize the definition of the ontology, offered a better interpretation of the data and optimized both the space memory and the execution time for exploiting this data., Comment: 10pages, 8 figures KEOD 2013, accepted but not enregistrement De: KEOD Secretariat [keod.secretariat@insticc.org] Envoy\'e: mardi 21 mai 2013 10:47 We are happy to inform you that the regular paper you have submitted to KEOD, with number 34, entitled "Automatic Ontology Generation for Data Mining Using FCA and Clustering", has been accepted as a Short Paper. arXiv admin note: text overlap with arXiv:1310.7829 by other authors

In this paper, we define a new structure analogous to group, called partial group. This structure concerns the partial stability by the composition inner law. We generalize the three isomorphism theorems for groups to partial groups.

We have applied harmonic expansion to derive an analytical solution for the Lorenz-Haken equations. This method is used to describe the regular and periodic self-pulsing regime of the single mode homogeneously broadened laser. These periodic solutions emerge when the ratio of the population decay rates is smaller than 0.11. We have also demonstrated the tendency of the Lorenz-Haken dissipative system to behave periodic for a characteristic pumping rate "2CP" [4], close to the second laser threshold "2C2th" (threshold of instability). When the pumping parameter "2C" increases, the laser undergoes a period-doubling sequence. This cascade of period doubling leads towards chaos. We study this type of solutions and indicate the zone of the control parameters for which the system undergoes irregular pulsing solutions. We had previously applied this analytical procedure to derive the amplitude of the first, third and the fifth order harmonics for the laser-field expansion [4, 14]. In this work, we extend this method in the aim of obtaining the higher harmonics. We show that this iterative method is indeed limited to the fifth order, and that above, the obtained analytical solution diverges from the numerical direct resolution of the equations., Comment: 20 pages, 4 figures, 1 annex

Imaging has occupied a huge role in the management of patients, whether hospitalized or not. Depending on the patients clinical problem, a variety of imaging modalities were available for use. This gave birth of the annotation of medical image process. The annotation is intended to image analysis and solve the problem of semantic gap. The reason for image annotation is due to increase in acquisition of images. Physicians and radiologists feel better while using annotation techniques for faster remedy in surgery and medicine due to the following reasons: giving details to the patients, searching the present and past records from the larger databases, and giving solutions to them in a faster and more accurate way. However, classical conceptual modeling does not incorporate the specificity of medical domain specially the annotation of medical image. The design phase is the most important activity in the successful building of annotation process. For this reason, we focus in this paper on presenting the conceptual modeling of the annotation of medical image by defining a new profile using the StarUML extensibility mechanism., Comment: 9 pages, 6 figures. In International Journal of Computer Applications, June 2013

In this paper, we define the complex dimension of any additive subgroup of R^{n}$which generalize the euclidien dimension given for the vector space. We give an explicit method to calculate this dimension.

In this paper, we give a characterization for any abelian subgroup G of a lie group of diffeomorphisms maps of C^n, having a somewhere dense orbit G(x), x in C^n: G(x) is somewhere dense in C^n if and only if there are f_{1},....,f_{2n+1 in exp^{-1}(G) such that f_{2n+1} in vect(f_{1},...,f_{2n}) and Z.f_{1}(x)+....+Z.f_{2n+1}(x) is dense subgroup of C^n, where vect(f_{1},....,f_{2n}) is the vector space over R generated by f_{1},....,f_{2n}.

We explain that the action-angle duality between the rational Ruijsenaars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the `Ruijsenaars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BC(n) generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure., Comment: Extended version of talk at the conference "Geometry, Integrability and Quantization XIV" (Varna, June 2012), 15 pages

In this paper, we introduce the notion of regular action of any abelian subgroup G of $Diff^{1}(C^n) on C^n (i.e. the closure of every orbit of G in some open set is a topological sub-manifold of C^n). We prove that if G fixes 0 and dim(vect(L_{G}) =n, then the action of G, can not be p-chaotic for every 0<= p <=n-1. (i.e. If G has a dense orbit then the set of all regular orbit with order p can not be dense in C^{n}), where vect(L_{G}) is the vector space generated by all Df_{0}, f in G. Moreover, weprove that the action of any abelian lie subgroup of Diff^{1}(C^{n}), is regular.

In this paper, we study the action on C^n of any group G of holomorphic diffeomorphisms (automorphisms) of C^n fixing 0. Suppose that there is x in C^n, having an orbit which generates C^n and also E(x)=C^n, where E(x) is the vector space generated by L_{G}={D_{0}fx, f in G }. We give an important condition so that an orbit G(x) is isomorphic (by linear map) to the orbit L_{G}(x)of the linear group L_{G}. More if G is abelian, we prove the existence of a G-invariant open set U, dense in C^n, in which every orbit O is relatively minimal (i.e. the closure of O in U is a closed non empty, G-invariant set and has no proper subset with these properties). Moreover, if G has a dense orbit in C^n then every orbit of U is dense in C^n.

In this paper we consider random Hamiltonians defined on long-range percolation graphs over $\ZZ^d$. The Hamiltonian consists of a randomly weighted Laplacian plus a random potential. We prove uniform existence of the integrated density of states and express the IDS using a Pastur-Shubin trace formula., Comment: 21 pages

The purpose of this paper is to study quadratic color Hom-Lie algebras. We present some constructions of quadratic color Hom-Lie algebras which we use to provide several examples. We describe $T^\ast$-extensions and central extensions of color Hom-Lie algebras and establish some cohomological characterizations.

In this paper, we give a characterization of the action of any abelian subgroup G of GL(n, C) on C^n. We prove that any orbit of G is regular with order m<=2n. Moreover, we give a method to determine this order. In the other hand, we specify the region of all orbits which are isomorphic. If G is finitely generated, this characterization is explicit.

A hyperbolic BC(n) Sutherland model involving three independent coupling constants that characterize the interactions of two types of particles moving on the half-line is derived by Hamiltonian reduction of the free geodesic motion on the group SU(n,n). The symmetry group underlying the reduction is provided by the direct product of the fixed point subgroups of two commuting involutions of SU(n,n). The derivation implies the integrability of the model and yields a simple algorithm for constructing its solutions., Comment: 14 pages, with minor modifications in v2

We give a characterization of hypercyclic finitely generated abelian semigroups of matrices on C^n using the extended limit sets (the J-sets). Moreover we construct for any n\geq 2 an abelian semigroup G of GL(n;C) generated by n + 1 diagonal matrices which is locally hypercyclic but not hypercyclic and such that JG(e_k) = C^n for every k = 1; : : : ; n, where (e_1; : : : ; e_n) is the canonical basis of C^n. This gives a negative answer to a question raised by Costakis and Manoussos., Comment: 10 pages

In this paper we study the action of non abelian subgroup G generated by affine homotheties on C^n. We prove that there exist a subgroup H of C\{0}, a G-invariant affine subspace E of C^n and b in E such that the closure of any orbit G(z) is equal to H(z-a)+E, z in C^n. In particular, every orbit in E is dense in it. Moreover, if the complementary U=C^n \E is non empty, every orbit of U is minimal in it.

In this paper, we give a characterization of hypercyclic abelian affine group G. If G is finitely generated, this characterization is explicit. We prove in particular that no abelian group generated by n affine maps on C^n has a dense orbit.

A homogeneous symmetric structure on an associative superalgebra A is a non-degenerate, supersymmetric, homogeneous (i.e. even or odd) and associative bilinear form on A. In this paper, we show that any associative superalgebra with non null product can not admit simultaneously even-symmetric and odd-symmetric structure. We prove that all simple associative superalgebras admit either even-symmetric or odd-symmetric structure and we give explicitly, in every case, the homogeneous symmetric structures. We introduce some notions of generalized double extensions in order to give inductive descriptions of even-symmetric associative superalgebras and odd-symmetric associative superalgebras. We obtain also an other interesting description of odd-symmetric associative superalgebras whose even parts are semi-simple bimodules without using the notions of double extensions.

We generalize to the case of Lie superalgebras the classical symplectic double extension of symplectic Lie algebras introduced in [2]. We use this concept to give an inductive description of nilpotent homogeneous-symplectic Lie superalgebras. Several examples are included to show the existence of homogeneous quadratic symplectic Lie superalgebras other than even-quadratic even-symplectic considered in [6]. We study the structures of even (resp. odd)-quadratic odd (resp. even)-symplectic Lie superalgebras and odd-quadratic odd-symplectic Lie superalgebras and we give its inductive descriptions in terms of quadratic generalized double extensions and odd quadratic generalized double extensions. This study complete the inductive descriptions of homogeneous quadratic symplectic Lie superalgebras started in [6]. Finally, we generalize to the case of homogeneous quadratic symplectic Lie superargebras some relations between even-quadratic even-symplectic Lie superalgebras and Manin superalgebras established in [6].