Natural Embedding Research Articles

VIRTUALIZATION MAP FOR THE LITTELMANN PATH MODEL

We show the natural embedding of weight lattices from a diagram folding is a virtualization map for the Littelmann path model, which recovers a result of Kashiwara. As an application, we give a type independent proof that certain Kirillov--Reshetikhin crystals respect diagram foldings, which is a known result on a special case of a conjecture given by Okado, Schilling, and Shimozono.

Entropy numbers of embeddings of Schatten classes

Let 0<p,q≤∞ and denote by SpN and SqN the corresponding finite-dimensional Schatten classes. We prove optimal bounds, up to constants only depending on p and q, for the entropy numbers of natural embeddings between SpN and SqN. This complements the known results in the classical setting of natural embeddings between finite-dimensional ℓp spaces due to Schütt, Edmunds–Triebel, Triebel and Guédon–Litvak/Kühn. We present a rather short proof that uses all the known techniques as well as a constructive proof of the upper bound in the range N≤n≤N2 that allows deeper structural insight and is therefore interesting in its own right. Our main result can also be used to provide an alternative proof of recent lower bounds in the area of low-rank matrix recovery.

Word Embeddings for User Profiling in Online Social Networks

User profiling in social networks can besignificantly augmented by using available full-text itemssuch as posts or statuses and ratings (in the form oflikes) that users give them. In this work, we applymodern natural language processing techniques basedon word embeddings to several problems related touser profiling in social networks. First, we present anapproach to create user profiles that measure a user’sinterest in various topics mined from the full texts of theitems. As a result, we get a user profile that can be used,e.g., for cold start recommendations for items, targetedadvertisement, and other purposes; our experimentsshow that the interests mining method performs on alevel comparable with collaborative algorithms while atthe same time being a cold start approach, i.e., itdoes not use the likes of an item being recommended.Second, we study the problem of predicting a user’sdemographic attributes such as age and gender basedon his or her full-text items. We evaluate theefficiency of various age prediction algorithms based onword2vec word embeddings and conduct an extensiveexperimental evaluation, comparing these algorithmswith each other and with classical baseline approaches.

The Shoda-completion of a Banach algebra

In stark contrast to the case of finite rank operators on a Banach space, the socle of a general, complex, semisimple and unital Banach algebra A may exhibit the ‘pathological’ property that not all traceless elements of the socle of A can be expressed as the commutator of two elements belonging to the socle. The aim of this paper is to show how one may develop an extension of A which removes the aforementioned problem. A naive way of achieving this is to simply embed A in the algebra of bounded linear operators on A, i.e. the natural embedding of A into . But this extension is so large that it may not preserve the socle of A in the extended algebra . Our proposed extension, which we shall call the Shoda-completion of A, is natural in the sense that it is small enough for the socle of A to retain the status of socle elements in the extension.

Binary linear codes, dimers and hypermatrices

We show that the weight enumerator of any binary linear code is equal to the permanent of a 3-dimensional hypermatrix (3-matrix). We also show that each permanent is a determinant of a 3-matrix. As an application we write the dimer partition function of a finite 3-dimensional cubic lattice as the determinant of the vertex-adjacency 3-matrix of a 2-dimensional simplicial complex which preserves the natural embedding of the cubic lattice. Keywords: Ising problem, dimer problem, partition function, perfect matching, Kasteleyn matrix, linear binary code, permanent, 3-dimensional cubic lattice, triangular configuration, 2-dimensional simplicial complex.

A Generalized Surface Hopping Algorithm To Model Nonadiabatic Dynamics near Metal Surfaces: The Case of Multiple Electronic Orbitals.

For a molecule with multiple electronic orbitals and many nuclear degrees of freedom near a metal surface, there is a natural embedding of the quantum-classical Liouville equation inside a classical master equation (QCLE-CME) to model nonadiabatic dynamics ( J. Chem. Phys. 2016 , 145 , 054102 ). In this paper, we propose a variety of surface hopping algorithms for solving such a QCLE-CME. We find that an augmented surface hopping (A-SH) algorithm works well for propagating such nonadiabatic dynamics (near a metal surface). We expect the present algorithm will be very useful for modeling electrochemical problems in the future.

Quantum B-algebras: their omnipresence in algebraic logic and beyond

Quantum B-algebras are implicational subreducts of quantales. Their ubiquity and unifying role in algebraic logic and beyond is discussed in a brief survey, with old and new examples included. A special section is devoted to CKL-algebras (alias HBCK-algebras). Using a natural embedding of any CKL-algebra into a semibrace, Cornish's identity is derived, which yields a new syntactic proof of Wronski's conjecture that CKL-algebras form a variety.

Vectorial Hankel operators, Carleson embeddings, and notions of BMOA

Let {textrm{BMOA}_{mathcal{N}mathcal{P}}left(mathcal{L}right)} denote the space of {mathcal{L}}-valued analytic functions {phi} for which the Hankel operator {Gamma_phi} is {H^2left(mathcal{H}right)}-bounded. Obtaining concrete characterizations of {textrm{BMOA}_{mathcal{N}mathcal{P}}left(mathcal{L}right)} has proven to be notoriously hard. Let {D^alpha} denote fractional differentiation. Motivated originally by control theory, we characterize {H^2left(mathcal{H}right)}-boundedness of {D^alphaGamma_phi}, where {alpha > 0}, in terms of a natural anti-analytic Carleson embedding condition. We obtain three notable corollaries: The first is that {textrm{BMOA}_{mathcal{N}mathcal{P}}left(mathcal{L}right)} is not characterized by said embedding condition. The second is that when we add an adjoint embedding condition, we obtain a sufficient but not necessary condition for boundedness of {Gamma_phi}. The third is that there exists a bounded analytic function for which the associated anti-analytic Carleson embedding is unbounded. As a consequence, boundedness of an analytic Carleson embedding does not imply that the anti-analytic ditto is bounded. This answers a question by Nazarov, Pisier, Treil, and Volberg.

Adaptive methods for stochastic differential equations via natural embeddings and rejection sampling with memory

Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs.

Norms in group algebras of finite groups under inducing

We compare norms of an element of a group algebra of a normal subgroup of a finite group in a representation of the normal subgroup and the corresponding induced representation (under the natural embedding of the group algebra of the normal subgroup in the group algebra of the entire group).

A Space of Phylogenetic Networks

A classical problem in computational biology is constructing a phylogenetic tree given a set of distances between $n$ species. In many cases, a tree structure is too constraining. We consider a split network, which is a generalization of a tree in which multiple parallel edges signify divergence. A geometric space of such networks is introduced, forming a natural extension of the familiar space of phylogenetic trees. We explore properties of the space of networks and construct a natural embedding of the compactification of the real moduli space of curves within it.

Generalized Hyperarithmetical Computability Over Structures

We consider the class of approximation spaces generated by admissible sets, in particular by hereditarily finite superstructures over structures. Generalized computability on approximation spaces is conceived of as effective definability in dynamic logic. By analogy with the notion of a structure Σ-definable in an admissible set, we introduce the notion of a structure effectively definable on an approximation space. In much the same way as the Σ-reducibility relation, we can naturally define a reducibility relation on structures generating appropriate semilattices of degrees of structures (of arbitrary cardinality), as well as a jump operation. It is stated that there is a natural embedding of the semilattice of hyperdegrees of sets of natural numbers in the semilattices mentioned, which preserves the hyperjump operation. A syntactic description of structures having hyperdegree is given.

The Littlewood-Richardson rule for wreath products with symmetric groups and the quiver of the category F≀FIn

ABSTRACTWe give a new proof for the Littlewood-Richardson rule for the wreath product F≀Sn where F is a finite group. Our proof does not use symmetric functions but use more elementary representation theoretic tools. We also derive a branching rule for inducing the natural embedding of F≀Sn to F≀Sn+1. We then apply the generalized Littlewood-Richardson rule for computing the ordinary quiver of the category F≀FIn where FIn is the category of all injective functions between subsets of an n-element set.

Derived equivalences for hereditary Artin algebras

We study the role of the Serre functor in the theory of derived equivalences. Let A be an abelian category and let (U,V) be a t-structure on the bounded derived category DbA with heart H. We investigate when the natural embedding H→DbA can be extended to a triangle equivalence DbH→DbA. Our focus of study is the case where A is the category of finite-dimensional modules over a finite-dimensional hereditary algebra. In this case, we prove that such an extension exists if and only if the t-structure is bounded and the aisle U of the t-structure is closed under the Serre functor.

COARSE REDUCIBILITY AND ALGORITHMIC RANDOMNESS

AbstractA coarse description of a set A ⊆ ω is a set D ⊆ ω such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse descriptions of a given set A, especially when A is effectively random in some sense. We show that if A is 1-random and B is computable from every coarse description D of A, then B is K-trivial, which implies that if A is in fact weakly 2-random then B is computable. Our main tool is a kind of compactness theorem for cone-avoiding descriptions, which also allows us to prove the same result for 1-genericity in place of weak 2-randomness. In the other direction, we show that if $A \le _{{\rm{T}}} \emptyset {\rm{'}}$ is a 1-random set, then there is a noncomputable c.e. set computable from every coarse description of A, but that not all K-trivial sets are computable from every coarse description of some 1-random set. We study both uniform and nonuniform notions of coarse reducibility. A set Y is uniformly coarsely reducible to X if there is a Turing functional Φ such that if D is a coarse description of X, then ΦD is a coarse description of Y. A set B is nonuniformly coarsely reducible to A if every coarse description of A computes a coarse description of B. We show that a certain natural embedding of the Turing degrees into the coarse degrees (both uniform and nonuniform) is not surjective. We also show that if two sets are mutually weakly 3-random, then their coarse degrees form a minimal pair, in both the uniform and nonuniform cases, but that the same is not true of every pair of relatively 2-random sets, at least in the nonuniform coarse degrees.

Unobstructed Stanley–Reisner degenerations for dual quotient bundles on G(2,n)

Let Q⁎ denote the dual of the quotient bundle on the Grassmannian G(2,n). We prove that the ideal of Q⁎ in its natural embedding has initial ideal equal to the Stanley–Reisner ideal of a certain unobstructed simplicial complex. Furthermore, we show that the coordinate ring of Q⁎ has no infinitesimal deformations for n>5.

The center of the affine nilTemperley–Lieb algebra

We give a description of the center of the affine nilTemperley–Lieb algebra based on a certain grading of the algebra and on a faithful representation of it on fermionic particle configurations. We present a normal form for monomials, hence construct a basis of the algebra, and use this basis to show that the affine nilTemperley–Lieb algebra is finitely generated over its center. As an application, we obtain a natural embedding of the affine nilTemperley–Lieb algebra on N generators into the affine nilTemperley–Lieb algebra on $$N+1$$ generators.

혼합증강현실에서 라이브 행동자와 실체 표현을 위한 표준 모델

/012345#2367458 9(:67&; 45#67458=?@A&BCB.  45 DE ? !#$(LAE: live actor and entity)63D 67F :=>GHIJ%K3LMN, OP3D QRS, 3D 67$TUV WHX 6Y=B. Z [  ?LAE83D 67F GHIJ=\, ] ]7^A_3*+&%) `(B. `(*+&/aM]LAES:7^A 3 K3LB.AbstractMixed and augmented reality technique deals with mixing content between real world and virtual world containing augmented reality and augmented virtuality excluding of pure real and pure virtual world. In mixed and augmented reality, if a live actor and entity moving in real world can be embedded more naturally in 3D virtual world, various advanced applications such 3D tele-presence, 3D virtual experience education and etc can be serviced. Therefore, in this paper, we propose a standard model which is supporting to embed the live actor and entity into 3D virtual space, and to interact with each other. And also the natural embedding and interaction of live actor and entity can be performed based on the proposed model. Keyword : Mixed and augmented reality, live actor and entity, spatial mapping, event mapping

Microstructure and tribological properties of MoS2+Zr composite coatings in high humidity environment

MoS2+Zr composite coatings with different Zr contents and their pure MoS2 counterparts were deposited on silicon wafers and steel substrates by closed field unbalanced magnetron sputtering system. The microstructure, mechanical and tribological properties of as-prepared coatings were systematically investigated using a number of analytical techniques and the effect of different Zr contents on tribological behaviors in humidity conditions of these as-deposited composite coatings was discussed. It is clearly uncovered from the present results that the MoS2+Zr composite coatings were amorphous nature embedding some nanocrystallites. Doping of MoS2 coatings with Zr can remarkably improve the mechanical and tribological properties of pure MoS2 coating in high humidity (68% RH) environment, rendering the coefficient of friction (COF) decreases with increasing Zr content. Additionally, MoS2+Zr composite coatings exhibit much more stable and lower friction coefficients with increasing applied load. The lowest friction coefficient of as-deposited MoS2+Zr composite coating was about 0.04 with an applied load of 20N (at 68% RH), where the friction coefficient of pure MoS2 coating was around 0.7. The improved tribological property of the MoS2+Zr composite coatings in high humidity environment was discussed in terms of the obtained lower friction coefficient, higher hardness and better adhesion of the composite coatings combined with inhibition of MoS2 oxidation.

The linear programming relaxation permutation symmetry group of an orthogonal array defining integer linear program

There is always a natural embedding of $S_{s}\wr S_{k}$ into the linear programming (LP) relaxation permutation symmetry group of an orthogonal array integer linear programming (ILP) formulation with equality constraints. The point of this paper is to prove that in the $2$-level, strength-$1$ case the LP relaxation permutation symmetry group of this formulation is isomorphic to $S_{2}\wr S_{k}$ for all $k$, and in the $2$-level, strength-$2$ case it is isomorphic to $S_{2}^{k}\rtimes S_{k+1}$ for $k\geqslant 4$. The strength-$2$ result reveals previously unknown permutation symmetries that cannot be captured by the natural embedding of $S_{2}\wr S_{k}$. We also conjecture a complete characterization of the LP relaxation permutation symmetry group of the ILP formulation.Supplementary materials are available with this article.