By the Choi matrix criteria it is easy to determine if a specific linear matrix map is completely positive, but to establish whether a linear matrix map is positive is much less straightforward. In ...this paper we consider classes of linear matrix maps, determined by structural conditions on an associated matrix, for which positivity and complete positivity coincide. The basis of our proofs lies in a representation of ⁎-linear matrix maps going back to work of R.D. Hill which enables us to formulate a sufficient condition in terms of surjectivity of certain bilinear maps.
Poset-causal systems form a class of decentralized systems introduced by Shah and Parrilo (47th IEEE conference on decision and control, IEEE, 2008) and studied mainly in the context of optimal ...decentralized control. In this paper, we develop part of the realization theory for poset-causal systems. More specifically, we investigate several notions of controllability and observability, and their relation under duality. These new notions extend concepts of controllability and observability in the context of coordinated linear systems (Kempker et al. in Linear Algebra Appl 437:121–167, 2012). While for coordinated linear systems there is a clear hierarchical structure with a single (main) coordinator, for poset-causal systems there need not be a single coordinator, and the communication structure between the decentralized systems allows for more intricate structures, governed by partial orders. On the other hand, we show that the class of poset-causal systems is closed under duality, which is not the case for coordinated linear systems, and that duality relations between the various notions of observability and controllability exist.
In 1994, H. Bart and V. É. Tsekanovskii posed the question whether the Banach space operator relations matricial coupling (MC), equivalence after extension (EAE) and Schur coupling (SC) coincide, ...leaving only the implication EAE/MC ⇒ SC open. Despite several affirmative results, in this paper we show that the answer in general is no. This follows from a complete description of EAE and SC for the case that the operators act on essentially incomparable Banach spaces, which also leads to a new characterisation of the notion of essential incomparability. Concretely, the forward shift operators U on ℓp and V on ℓq, for 1⩽p,q⩽∞, p≠q, are EAE but not SC. As a corollary, SC is not transitive. Under mild assumptions, given U and V that are Atkinson or generalised invertible and EAE, we give a concrete operator W that is SC to both U and V, even if U and V are not SC themselves. Some further affirmative results for the case where the Banach spaces are isomorphic are also obtained.
In the paper (Hill, 1973) from 1973 R.D. Hill studied linear matrix maps L:ℂq×q→ℂn×n which map Hermitian matrices to Hermitian matrices, or equivalently, preserve adjoints, i.e., L(V∗)=L(V)∗, via ...representations of the form L(V)=∑k,l=1mHklAlVAk∗,V∈ℂq×q,for matrices A1,…,Am∈ℂn×q and continued his study of such representations in later work, sometimes with co-authors, to completely positive matrix maps and associated matrix reorderings. In this paper we expand the study of such representations, referred to as Hill representations here, in various directions. In particular, we describe which matrices A1,…,Am can appear in Hill representations (provided the number m is minimal) and determine the associated Hill matrix H=Hkl explicitly. Also, we describe how different Hill representations of L (again with m minimal) are related and investigate further the implication of ∗-linearity on the linear map L.
The bounded real lemma (BRL) is a classical result in systems theory, which provides a linear matrix inequality criterium for dissipativity, via the Kalman-Yakubovich-Popov (KYP) inequality. The BRL ...has many applications, among others in
H
∞
control. Extensions to infinite dimensional systems, although already present in the work of Yakubovich, have only been studied systematically in the last few decades. In this context various notions of stability, observability and controllability exist, and depending on the hypothesis one may have to allow the KYP-inequality to have unbounded solutions which forces one to consider the KYP-inequality in a spatial form. In the present paper we consider the BRL for continuous time, infinite dimensional, linear well-posed systems. Via an adaptation of Willems’ storage function approach we present a unified way to address both the standard and strict forms of the BRL. We avoid making use of the Cayley transform and work only in continuous time. While for the standard bounded real lemma, we obtain analogous results as there exist for the discrete time case, when treating the strict case additional conditions are required, at least at this stage. This might be caused by the fact that the Cayley transform does not preserve exponential stability, an important property in the strict case, when transferring a continuous-time system to a discrete-time system.
Infantile fibrosarcoma (IFS) and congenital mesoblastic nephroma (CMN) are locally aggressive tumors primarily occurring in infants. Both IFS and the cellular subtype of CMN show overlapping ...morphological features and an ETV6-NTRK3 fusion, suggesting a close relationship. An activating alteration of EGFR, based on an EGFR kinase domain duplication (KDD), occurs in a subset of CMNs lacking an NTRK3 rearrangement, especially in the classic and mixed type. So far no EGFR-KDDs have been detected in IFS.
We describe four pediatric tumors at the extremities (leg, n = 2; foot and arm n = 1) with histological features of IFS/CMN. Two cases showed classic IFS morphology while two were similar to classic/mixed type CMN. In all cases, an EGFR-KDD was identified without detection of a fusion gene. There were no abnormalities of the kidneys in any of the patients.
This is the first description of IFS with an EGFR-KDD as driver mutation, supporting that IFS and CMN are similar lesions with the same morphological and genetic spectrum. Pathologists should be aware of the more fibrous variant of IFS, similar to classic/mixed type CMN. Molecular analyses are crucial to treat these lesions adequately, especially with regard to the administration of tyrosine kinase inhibitors.
•Infantile fibrosarcoma (IFS) without a fusion gene may carry an EGFR kinase domain duplication.•This leads to activation of the EGFR-related pathways.•IFS is morphologically similar to congenital mesoblastic nephroma (CMN).•Therefore, IFS and CMN represent the same tumor at different locations.•They belong to the receptor protein kinase – soft tissue tumor family.
Objective
To determine in a cohort of young patients with suspected axial spondyloarthritis (axSpA), the prevalence of lumbosacral transitional vertebra (LSTV), its association with local bone marrow ...edema (BME) and lumbar spine degeneration, and the potential relationship with MRI findings and clinical signs of axSpA.
Materials and methods
Baseline imaging studies and clinical information of patients from the SPondyloArthritis Caught Early-cohort (back pain ≥3 months, ≤2 years, onset <45 years) were used. Two independent readers assessed all patients for LSTV on radiography, and BME-like and degenerative changes on MRI. Patients with and without LSTV were compared with regard to the prevalence of MRI findings and the results of clinical assessment using Chi-squared test or
t
test.
Results
Of 273 patients (35.1% male, mean age 30.0), 68 (25%) patients showed an LSTV, without statistical significant difference between patients with and without axSpA (
p
= 0.327). Local sacral BME was present in 9 out of 68 (13%) patients with LSTV and absent in patients without LSTV (
p
< 0.001). Visual analogue scale (VAS) pain score and spinal mobility assessments were comparable.
Conclusions
LSTV is of low clinical relevance in the early diagnosis of axSpA. There is no difference between patients with and without LSTV regarding the prevalence of axSpA, pain and spinal mobility, and a BME-like pattern at the pseudoarticulation does not reach the SI joints.
Motivated by work of Yu.L. Shmul'yan a pre-order and an equivalence relation on the set of operator-valued Schur class functions are introduced and the behavior of Redheffer linear fractional ...transformations (LFTs) with respect to these relations is studied. In particular, it is shown that Redheffer LFTs preserve the equivalence relation, but not necessarily the pre-order. The latter does occur under some additional assumptions on the coefficients in the Redheffer LFT.
This paper concerns the analysis of an unbounded Toeplitz-like operator generated by a rational matrix function having poles on the unit circle
T
. It extends the analysis of such operators generated ...by scalar rational functions with poles on
T
found in Groenewald et al. (Oper Theory Adv Appl 271:239–268, 2018; Oper Theory Adv Appl 272:133–154, 2019; Integr Equ Oper Theory 91, 2019). A Wiener–Hopf type factorization of rational matrix functions with poles and zeroes on
T
is proved and then used to analyze the Fredholm properties of such Toeplitz-like operators. A formula for the index, based on the factorization, is given. Furthermore, it is shown that the determinant of the matrix function having no zeroes on
T
is not sufficient for the Toeplitz-like operator to be Fredholm, in contrast to the classical case.
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