Weak index pairs and the Conley index for discrete multivalued dynamical systems. Part II: properties of the index

Motivation to revisit the Conley index theory for discrete multivalued dynamical systems stems from the needs of broader real applications, in particular in sampled dynamics or in combinatorial dynamics. The new construction of the index in [B. Batko and M. Mrozek, {\em SIAM J. Applied Dynamical Systems}, 15(2016), pp. 1143-1162] based on weak index pairs, under the circumstances of the absence of index pairs caused by relaxing the isolation property, seems to be a promising step towards this direction. The present paper is a direct continuation of [B. Batko and M. Mrozek, {\em SIAM J. Applied Dynamical Systems}, 15(2016), pp. 1143-1162] and concerns properties of the index defined therin, namely Wa\.zewski property, the additivity property, the homotopy (continuation) property and the commutativity property. We also present the construction of weak index pairs in an isolating block

Weak index pairs and the Conley index for discrete multivalued dynamical systems

Motivated by the problem of reconstructing dynamics from samples we revisit the Conley index theory for discrete multivalued dynamical systems. We introduce a new, less restrictive definition of the isolating neighbourhood. It turns out that then the main tool for the construction of the index, i.e. the index pair, is no longer useful. In order to overcome this obstacle we use the concept of weak index pairs

On Approximate Solutions of Functional Equations in Vector Lattices

We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra). The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations. The idea is based on the use of the Spectral Representation Theory for Riesz spaces. The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y)+F(x)+F(y)≠0⇒F(x+y)=F(x)+F(y) in Riesz spaces, the Cauchy equation with squares F(x+y)2=(F(x)+F(y))2 in f-algebras, and the quadratic functional equation F(x+y)+F(x-y)=2F(x)+2F(y) in Riesz spaces

Physician adherence to treat-to-target and practice guidelines in rheumatoid arthritis

Principles of treat-to-target (T2T) have been widely adopted in both multinational and regional guidelines for rheumatoid arthritis (RA). Several questionnaire studies among physicians and real-world data have suggested that an evidence–practice gap exists in RA management. Investigating physician adherence to T2T, which requires a process measure, is difficult. Different practice patterns among physicians are observed, while adherence to protocolized treatment declines over time. Rheumatologist awareness, agreement, and claims of adherence to T2T guidelines are not always consistent with medical records. Comorbidities, a difficult disease course, communication barriers, and individual preferences may hinder an intensive, proactive treatment stance. Interpreting deviations from protocolized treatment/T2T guidelines requires sufficient clinical context, though higher adherence seems to improve clinical outcomes. Nonmedical constraints in routine care may consist of barriers in healthcare structure and socioeconomic factors. Therefore, strategies to improve the institution of T2T should be tailored to local healthcare. Educational interventions to improve T2T adherence among physicians may show a moderate, although beneficial effect. Meanwhile, a proportion of patients with inadequately controlled RA exists, while management decisions may not be in accordance with T2T. Physicians tend to be aware of current guidelines, but their institution in routine practice seems challenging, which warrants attention and further study

Stability of the exponential functional equation in Riesz algebras

We deal with the stability of the exponential Cauchy functional equation ( + ) = ( ) ( ) in the class of functions : → mapping a group ( , +) into a Riesz algebra . The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem

Linking combinatorial and classical dynamics : Conley index and Morse decompositions

We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a multivalued dynamical system F on the geometric realization of the simplicial complex. Moreover, F may be chosen in such a way that the isolated invariant sets, Conley indices, Morse decompositions and Conley–Morse graphs of the combinatorial vector field give rise to isomorphic objects in the multivalued map case

Newly developed cardiovascular risk factors in rheumatoid arthritis patients initiating biologic treatment

Introduction: Rheumatoid arthritis (RA) is a risk factor (RF) for cardiovascular (CV) disease, a leading cause of mortality in RA patients. Material and methods: Consecutive records of RA patients with high disease activity screened upon biologic therapy initiation were reviewed between January 2001 and 2018. Patients with at least 6-month follow-up and baseline disease activity scores were enrolled (n = 353) and stratified into manifest CV disorder (“overt CVD”), any traditional CV risk factor (“atCVrisk”) and no CV risk factor (“vlCVrisk”) groups. Results: Overall, mean (SD) patient age was 51.4 (±12.2) years, and 291 (82.4%) subjects were female. Median follow-up was 41.9 (IQR 18.6, 80) months. Overall, 89 (25.2%) individuals developed at least one new CV RF, of which 65 (18.4%) acquired one and 24 (6.8%) two or more. Incident lipid disorders (42, 11.9%), followed by hypertension (14, 4%), atrial fibrillation (17, 4.8%) and venous thromboembolism (VTE) (16, 4.5%), were common. Incident major adverse cardiac events (MACE) were not reported in the vlCVrisk group, in contrast to atCVrisk (n = 8, 4.2%) or overt CVD (n = 4, 18.2%). Age was a significant predictor of incident CV risk factor (HR 1.04, 95% CI: 1.02–1.07; p < 0.01). In age-adjusted analyses, only baseline body mass index (BMI) (HR 1.11, 95% CI: 1.04–1.18; p < 0.01), but not ever smoking (p = 0.93), male sex (p = 0.26), positive RF (p = 0.24), positive ACPA (p = 0.90), or baseline disease activity (p = 0.19), were independent predictor of incident CV risk factors. Conclusions: Patients with RA initiating biologics should be screened for cardiometabolic risk factors, especially at an older age. The presence of at least one risk factor may be linked to a worse long-term prognosis

Venopunkcja żyły odłokciowej jako alternatywne podejście dla oceny stężenia CGRP w osoczu krwi u pacjentów z dysfunkcją układu ruchowego narządu żucia

Introduction: Calcitonin gene-related peptide is an important vasodilator. It plays an important role in the metabolism of chewing muscles. The aim of the study was to evaluate the plasma level of CGRP in patients with myofascial pain (RDC/TMD Ia) and myofascial pain with limited opening (RDC/TMD Ib) before and after occlusal splint therapy (Michigan splint). Material and methods: A randomised trial was performed including 39 patients (males = 3, females = 36). Blood samples were taken from the external jugular vein (JUG) and cubital vein (CUB) before and after 30 days of occlusal splint therapy. Plasma levels of CGRP were measured with ELISA KIT for Human Calcitonin Gene Related Peptide (CGRP) 96T (USCNK Business Co. Ltd.). Results: The results of the study show that the plasma CGRP level was higher in the external jugular vein (JUG1 = 5.07pg/mL [SD = 1.99]) than in cubital vein (CUB1 = 4.3 pg/mL [SD = 1.6]). After 30 days of the occlusal splint therapy the levels in both veins increased: JUG2 = 6.07 pg/mL (SD = 2.19), and CUB2 = 4.9 pg/mL (SD = 1.4). The CGRP plasma level increase was statistically significant only in the external jugular vein (JUG) (p &lt; 0.05). Statistically significant pain intensity reduction was observed: VAS1 = 5.4 (SD = 2.08) decreased to VAS2 = 1.7 (SD = 2.07) after splint therapy (p &lt; 0.05). Conclusions: Venepuncture of an external jugular vein is more precise, than venepuncture of a cubital vein in evaluating CGRP plasma level changes in patients with TMD.Wstęp: Peptyd pochodny genu kalcytoniny jest ważną substancja naczynio-rozkurczową. Odgrywa ważną role w metabolizmie mięśni żucia. Celem pracy była ocena stężenia osoczowego CGRP u pacjentów z bólem mięśniowo-powięziowym (RDC/TMD Ia) oraz z bólem mięśniowo-powięziowym z ograniczonym odwodzeniem (RDC/TMD Ib), przed i po terapii szyną okluzyjną (Szyna Michigan). Materiał i metody: Przeprowadzono badanie randomizowane, do którego włączono 39 pacjentów (mężczyźni = 3, kobiety = 36). Próbki krwi pobrano z żyły szyjnej zewnętrznej (JUG) oraz z żyły odłokciowej (CUB), przed leczeniem i po 30 dniach stosowania szyny okluzyjnej. Stężenie neuropeptydu CGRP oceniano za pomocą zestawu ELISA KIT for Human Calcitonin Gene Related Peptide (CGRP) 96T (USCNK Business Co. Ltd.). Wyniki: Stwierdzono, że stężenie neuropeptydu CGRP było wyższe w materiale pobranym z żyły szyjnej zewnętrznej JUG1 = 5,07pg/ ml (SD = 1,99), niż w materiale pobranym z żyły odłokciowej CUB1 = 4,3 pg/ml (SD = 1,6). Po 30 dniach terapii szyną okluzyjną średnie stężenie CGRP w obu grupach CUB i JUG wzrosły: JUG2 = 6,07 pg/ml (SD = 2,19) i CUB2 = 4,9 pg/ml (SD = 1,4). Wzrost stężenia CGRP w osoczu krwi był istotny statystycznie jedynie w materiale pobranym z żyły szyjnej zewnętrznej (JUG) (p &lt; 0,05). Zaobserwowano także istotną statystycznie redukcję natężenia dolegliwości bólowych w skali VAS: VAS1 = 5,4 (SD = 2,08) redukcja do VAS2 = 1,7 (SD = 2.07), po przeprowadzonej szynoterapii (p &lt; 0,05). Wnioski: Wenopunkcja żyły szyjnej zewnętrznej dostarcza bardziej precyzyjnych pomiarów stężenia neuropeptydu CGRP w osoczu niż wenopunkcja żyły odłokciowej, u pacjentów z bólową postacią dysfunkcji narządu żucia

Zapalenie palców jako objaw chorobowy występujący nie tylko w spondyloartropatii zapalnej

  W praktyce reumatologicznej najczęściej spotykamy się z zapaleniem palców w przebiegu spondyloartropatii zapalnej; nie możemy jednak zapomnieć, że nie jest to jedyna jednostka chorobowa, w której występuje ten objaw. To ważne, ponieważ mimo wspólnego mianownictwa leczenie jest różne w zależności od etiologii. Niniejsza praca ma na celu zapoznanie czytelników z innymi przyczynami zapalenia palców. Forum Reumatol. 2016, tom 2, nr 3: 106–110