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For positive integers $i_1,...,i_k$ with $i_1 > 1$, we define the multiple $t$-value $t(i_1,...,i_k)$ as the sum of those terms in the usual infinite series for the multiple zeta value $ζ(i_1,...,i_k)$ with odd denominators. Like the multiple zeta values, the multiple $t$-values can be multiplied according to the rules of the harmonic algebra. Using this fact, we obtain explicit formulas for multiple $t$-values of repeated arguments analogous to those known for multiple zeta values. Multiple $t$-values can be written as rational linear combinations of the alternating or "colored" multiple zeta values. Using known results for colored multiple zeta values, we obtain tables of multiple $t$-values through weight 7, suggesting some interesting conjectures, including one that the dimension of the rational vector space generated by weight-$n$ multiple $t$-values has dimension equal to the $n$th Fibonacci number. We express the generating function of the height one multiple $t$-values $t(n,1,...,1)$ in terms of a generalized hypergeometric function. We also define alternating multiple $t$-values and prove some results about them.

We generalize the definition of truncated multiple zeta values by allowing arbitrary integers as arguments. This leads to interesting identities, particularly with the argument 0. Truncated multiple zeta values satisfy the same quasi-shuffle algebraic identities as multiple zeta values, but we need to extend the algebra QSym of quasi-symmetric functions to a larger algebra. Using this algebra, we are able to sum systematically powers of harmonic and generalized harmonic numbers. This leads to summation identities such as \[ \sum_{n=1}^\infty H_n^3\bigg(ζ(2)-\sum_{k=1}^n\frac{1}{k^2}-\frac{1}{n}\bigg)= -\frac{11}2ζ(4)+ζ(3)+3ζ(2)-6. \] We also prove analogous identities involving alternating sums of harmonic numbers and their powers.

Bestvina-Feighn-Handel show that for finitely many generic and independent hyperbolic automorphisms $φ_1, \cdots, φ_r$ of $F_n$, the resulting extension $F_n \rtimes F_r$ is hyperbolic. This paper generalizes the above statement to the case where $φ_1, \cdots, φ_r$ are hyperbolic non-surjective endomorphisms of $F_n$. In our case the output is a multiple HNN extension associated to a graph with one vertex and $r$ edges. All edge and vertex groups are isomorphic to $F_n$.

In this paper, we propose a deep multiple description coding framework, whose quantizers are adaptively learned via the minimization of multiple description compressive loss. Firstly, our framework is built upon auto-encoder networks, which have multiple description multi-scale dilated encoder network and multiple description decoder networks. Secondly, two entropy estimation networks are learned to estimate the informative amounts of the quantized tensors, which can further supervise the learning of multiple description encoder network to represent the input image delicately. Thirdly, a pair of scalar quantizers accompanied by two importance-indicator maps is automatically learned in an end-to-end self-supervised way. Finally, multiple description structural dissimilarity distance loss is imposed on multiple description decoded images in pixel domain for diversified multiple description generations rather than on feature tensors in feature domain, in addition to multiple description reconstruction loss. Through testing on two commonly used datasets, it is verified that our method is beyond several state-of-the-art multiple description coding approaches in terms of coding efficienc

Spatial division multiple access (SDMA) is essential to improve the spectrum efficiency for multi-user multiple-input multiple-output (MIMO) communications. The classical SDMA for massive MIMO with hybrid precoding heavily relies on the angular orthogonality in the far field to distinguish multiple users at different angles, which fails to fully exploit spatial resources in the distance domain. With dramatically increasing number of antennas, extremely large-scale antenna array (ELAA) introduces additional resolution in the distance domain in the near field. In this paper, we propose the concept of location division multiple access (LDMA) to provide a new possibility to enhance spectrum efficiency. The key idea is to exploit extra spatial resources in the distance domain to serve different users at different locations (determined by angles and distances) in the near field. Specifically, the asymptotic orthogonality of beam focusing vectors in the distance domain is proved, which reveals that near-field beam focusing is able to focus signals on specific locations to mitigate inter-user interferences. Simulation results verify the superiority of the proposed LDMA over classical SDMA

Background: Gait and balance impairment can profoundly impact people with multiple sclerosis (PwMS). Objectives: To evaluate the analytical and clinical validity of the U-Turn Test (UTT), a smartphone-based assessment of dynamic balance in PwMS. Methods: The GaitLab study (ISRCTN15993728) enrolled adult PwMS (EDSS 0.0-6.5). PwMS performed the UTT in a gait laboratory (supervised) using 6 smartphones at different wear locations and daily during a two-week remote period (unsupervised) using one smartphone (belt front). Median turn speed was computed per UTT. In the supervised setting, turn detection accuracy of smartphones was compared to motion capture (mocap) via F1 scores. Agreement between smartphone- and mocap-derived turn speed was assessed by Bland-Altman and ICC(3,1). In the unsupervised setting, test-retest reliability (ICC[2,1]) and correlations with Timed 25-Foot Walk (T25FW), EDSS, Ambulation Score, 12-item Multiple Sclerosis Walking Scale (MSWS-12), and Activities-specific Balance Confidence scale (ABC) were evaluated. Results: Ninety-six PwMS were included. Turn speed was comparable across supervised (1.44 rad/s) and unsupervised settings (1.47 rad/s). In the supervised

The central challenges in missing data models concern the identifiability of two distributions: the target law and the full law. The target law refers to the joint distribution of the data variables, whereas the full law refers to the joint distribution of the data variables and their corresponding response indicators. However, the relationship between the identifiability of these two distributions and the feasibility of multiple imputation has not been clearly established. We present a procedure where the choice of the imputation method is guided by identifiability considerations. We show that imputations can be drawn from the correct conditional distributions for all possible missing data patterns if and only if the full law is identifiable. This result implies that standard multiple imputation methods -- which keep observed values unchanged and replace missing values with imputed values -- are invalid when the target law is identifiable but the full law is not. We demonstrate that alternative imputation strategies can sometimes enable the estimation of the target law in such cases. Specifically, we introduce factorizable imputation where certain observed values are also imputed

In this paper we define multiple Dedekind zeta values (MDZV), using a new type of iterated integrals, called iterated integrals on a membrane. One should consider MDZV as a number theoretic generalization of Euler's multiple zeta values. Over imaginary quadratic fields MDZV capture, in particular, multiple Eisenstein series (Gangl, Kaneko and Zagier). We give an analogue of multiple Eisenstein series over real quadratic field and an alternative definition of values of multiple Eisenstein-Kronecker series (Goncharov). Each of them is a special case of multiple Dedekind zeta values. MDZV are interpolated into functions that we call multiple Dedekind zeta functions (MDZF). We show that MDZF have integral representation, can be written as infinite sum, and have analytic continuation. We compute explicitly the value of a multiple residue of certain MDZF over a quadratic number field at the point (1,1,1,1). Based on such computations, we state two conjectures about MDZV.

We obtain formulas relating $p$-adic cyclotomic multiple zeta values and cyclotomic multiple harmonic sums. In particular, we obtain a series formula for $p$-adic cyclotomic multiple zeta values, and conversely a formula for certain cyclotomic multiple harmonic sums in terms of $p$-adic cyclotomic multiple zeta values. Our formulas are related to the motivic framework via a new notion which we call pro-unipotent harmonic actions, which are ad hoc $p$-adic byproducts of the Ihara action. As an application, we prove a conjecture of Akagi, Hirose and Yasuda on the relation between $p$-adic multiple zeta values and multiple harmonic sums, and we generalize it to the cyclotomic case. We also deduce bounds on the dimension of the spaces of finite cyclotomic multiple zeta values.

Multiple antenna technologies have attracted large research interest for several decades and have gradually made their way into mainstream communication systems. Two main benefits are adaptive beamforming gains and spatial multiplexing, leading to high data rates per user and per cell, especially when large antenna arrays are used. Now that multiple antenna technology has become a key component of the fifth-generation (5G) networks, it is time for the research community to look for new multiple antenna applications to meet the immensely higher data rate, reliability, and traffic demands in the beyond 5G era. We need radically new approaches to achieve orders-of-magnitude improvements in these metrics and this will be connected to large technical challenges, many of which are yet to be identified. In this survey paper, we present a survey of three new multiple antenna related research directions that might play a key role in beyond 5G networks: Cell-free massive multiple-input multiple-output (MIMO), beamspace massive MIMO, and intelligent reflecting surfaces. More specifically, the fundamental motivation and key characteristics of these new technologies are introduced. Recent techn

Spatial division multiple access (SDMA) is essential to improve the spectrum efficiency for multi-user multiple-input multiple-output (MIMO) communications. The classical SDMA for massive MIMO with hybrid precoding heavily relies on the angular orthogonality in the far field to distinguish multiple users at different angles, which fails to fully exploit spatial resources in the distance domain. With the dramatically increasing number of antennas, the extremely large-scale antenna array (ELAA) introduces additional resolution in the distance domain in the near field. In this paper, we propose the concept of location division multiple access (LDMA) to provide a new possibility to enhance spectrum efficiency compared with classical SDMA. The key idea is to exploit extra spatial resources in the distance domain to serve different users at different locations (determined by angles and distances) in the near field. Specifically, the asymptotic orthogonality of near-field beam focusing vectors in the distance domain is proved, which reveals that near-field beam focusing is able to focus signals on specific locations with limited leakage energy at other locations. This special property cou

Rate-Splitting Multiple Access (RSMA) for multi-user downlink operates by splitting the message for each user equipment (UE) into a private message and a set of common messages, which are simultaneously transmitted by means of superposition coding. The RSMA scheme can enhance throughput and connectivity as compared to conventional multiple access techniques by optimizing the rate-splitting ratios along with the corresponding downlink beamforming vectors. This work examines the impact of erroneous channel state information (CSI) on the performance of RSMA in cell-free multiple-input multiple-output (MIMO) systems. An efficient robust optimization algorithm is proposed by using closed-form lower bound expressions on the expected data rates. Extensive numerical results show the importance of robust design in the presence of CSI errors and how the performance gain of RSMA over conventional schemes is affected by CSI imperfection.

Multiple Eisenstein series are holomorphic functions in the complex upper-half plane, which can be seen as a crossbreed between multiple zeta values and classical Eisenstein series. They were originally defined by Gangl-Kaneko-Zagier in 2006, and since then, many variants and regularizations of them have been studied. They give a natural bridge between the world of modular forms and multiple zeta values. In this note, we give a new algebraic interpretation of stuffle regularized multiple Eisenstein series based on the Hopf algebra structure of the harmonic algebra introduced by Hoffman.

We introduce adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values. They are two variants of cyclotomic multiple zeta values, closely related to each other. They arise as key tools for the study of $p$-adic cyclotomic multiple zeta values. Moreover, cyclotomic multiple harmonic values provide an adelic lift to a cyclotomic generalization of finite multiple zeta values. We establish certain standard properties of these two objects. We consider two types of properties : some related to double shuffle relations, and some related to associator and Kashiwara-Vergne relations.

We define and apply a method to study the non-vanishing of $p$-adic cyclotomic multiple zeta values. We prove the non-vanishing of certain cyclotomic multiple harmonic sums, and, via a formula proved in another paper, which expresses a cyclotomic multiple harmonic sums as an infinite sum of products of $p$-adic cyclotomic multiple zeta values, this implies the non-vanishing of certain $p$-adic cyclotomic multiple zeta values.

Multiple orthogonal polynomials with respect to two weights on the step-line are considered. A connection between different dual spectral matrices, one banded (recursion matrix) and one Hessenberg, respectively, and the Gauss-Borel factorization of the moment matrix is given. It is shown a hidden freedom exhibited by the spectral system related to the multiple orthogonal polynomials. Pearson equations are discussed, a Laguerre-Freud matrix is considered, and differential equations for type I and II multiple orthogonal polynomials, as well as for the corresponding linear forms are given. The Jacobi-Piñeiro multiple orthogonal polynomials of type I and type II are used as an illustrating case and the corresponding differential relations are presented. A permuting Christoffel transformation is discussed, finding the connection between the different families of multiple orthogonal polynomials. The Jacobi-Piñeiro case provides a convenient illustration of these symmetries, giving linear relations between different polynomials with shifted and permuted parameters. We also present the general theory for the perturbation of each weight by a different polynomial or rational function aka cal

Due to the explosive growth in the number of wireless devices and diverse wireless services, such as virtual/augmented reality and Internet-of-Everything, next generation wireless networks face unprecedented challenges caused by heterogeneous data traffic, massive connectivity, and ultra-high bandwidth efficiency and ultra-low latency requirements. To address these challenges, advanced multiple access schemes are expected to be developed, namely next generation multiple access (NGMA), which are capable of supporting massive numbers of users in a more resource- and complexity-efficient manner than existing multiple access schemes. As the research on NGMA is in a very early stage, in this paper, we explore the evolution of NGMA with a particular focus on non-orthogonal multiple access (NOMA), i.e., the transition from NOMA to NGMA. In particular, we first review the fundamental capacity limits of NOMA, elaborate on the new requirements for NGMA, and discuss several possible candidate techniques. Moreover, given the high compatibility and flexibility of NOMA, we provide an overview of current research efforts on multi-antenna techniques for NOMA, promising future application scenarios

Discussion of the designation of multiple-star components leads to a conclusion that, apart from components, we need to designate systems and centers-of-mass. The hierarchy is coded then by simple links to parent. This system is adopted in the multiple star catalogue, now available on-line. A short review of multiple-star statistics is given: the frequency of different multiplicities in the field, periods of spectroscopic sub-systems, relative orbit orientation, empirical stability criterion, and period-period diagram with its possible connection to formation of multiple stars.